Digital Electronics- An Introduction to Theory and Practice_W. H. Gothmann

8/18/2019 Digital Electronics- An Introduction to Theory and Practice_W. H. Gothmann

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Scilab Textbook Companion for

Digital Electronics: An Introduction To

Theory And Practice

by W. H. Gothmann1

Created byAritra Ray

B.TechElectronics Engineering

NIT-DURGAPUR

College TeacherProf. Sabyasachi Sengupta,iit-kharagpur

Cross-Checked byLavitha M. Pereira

November 11, 2013

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the ”Textbook Companion Project”section at the website http://scilab.in


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Book Description

Title: Digital Electronics: An Introduction To Theory And Practice

Author: W. H. Gothmann

Publisher: Prentice Hall Of India Pvt. Ltd., New Delhi

Edition: 2

Year: 1994

ISBN: 81-203-0348-2

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Scilab numbering policy used in this document and the relation to theabove book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

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Contents

List of Scilab Codes 4

2 Number Systems 7

3 Binary Codes 42

4 Boolean Algebra 58

6 Combinational Logic 62

11 Analog Digital Conversion 97

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List of Scilab Codes

Exa 2.1 Convert 10111 to decimal . . . . . . . . . . . . . . . . 7Exa 2.2 Convert 1011101001 to decimal . . . . . . . . . . . . . 7Exa 2.3 Convert 110111 to decimal . . . . . . . . . . . . . . . 8Exa 2.4 Convert 43 to binary . . . . . . . . . . . . . . . . . . . 8Exa 2.5 Convert 200 to binary . . . . . . . . . . . . . . . . . . 8Exa 2.6 Convert 43 to binary . . . . . . . . . . . . . . . . . . . 8Exa 2.7 Convert 200 to binary . . . . . . . . . . . . . . . . . . 9Exa 2.8 Add 1011 and 110 . . . . . . . . . . . . . . . . . . . . 9Exa 2.9 Add 11110 and 11 . . . . . . . . . . . . . . . . . . . . 10Exa 2.10 Subtract one from 100 . . . . . . . . . . . . . . . . . . 10Exa 2.11 Multiply 1011 by 101 . . . . . . . . . . . . . . . . . . 11Exa 2.12 Multiply 11010 by 11011 . . . . . . . . . . . . . . . . . 11Exa 2.13 Divide 110110 by 101 . . . . . . . . . . . . . . . . . . 12

Exa 2.14 Convert 1010111010 to hexadecimal . . . . . . . . . . 12Exa 2.15 Convert 11011110101110 to hexadecimal . . . . . . . . 13Exa 2.16 Convert 4A8C to binary . . . . . . . . . . . . . . . . . 13Exa 2.17 Convert FACE to binary . . . . . . . . . . . . . . . . . 14Exa 2.18 Convert 2C9 to decimal . . . . . . . . . . . . . . . . . 14Exa 2.19 Convert EB4A to decimal . . . . . . . . . . . . . . . . 14Exa 2.20 Convert 423 to hexadecimal . . . . . . . . . . . . . . . 14Exa 2.21 Convert 72905 to hexadecimal . . . . . . . . . . . . . 15Exa 2.22 Add 1A8 and 67B . . . . . . . . . . . . . . . . . . . . 15Exa 2.23 Add ACEF1 and 16B7D . . . . . . . . . . . . . . . . . 16Exa 2.24 Subtract 3A8 from 1273 . . . . . . . . . . . . . . . . . 16

Exa 2.25 Multiply 1A3 by 89 . . . . . . . . . . . . . . . . . . . 17Exa 2.26 Divide 1EC87 by A5 . . . . . . . . . . . . . . . . . . . 17Exa 2.27 Convert 11111011110101 to octal . . . . . . . . . . . . 18Exa 2.28 Convert 1011110100011000111 to octal . . . . . . . . . 18

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Exa 2.29 Convert octal number 3674 to binary . . . . . . . . . . 19

Exa 2.30 Minus 5 in twos complement form . . . . . . . . . . . 19Exa 2.31 12 bit twos complement . . . . . . . . . . . . . . . . . 20Exa 2.32 16 bit twos complement . . . . . . . . . . . . . . . . . 20Exa 2.33 Twos complement of minus4 second method . . . . . . 21Exa 2.34 Twos complement of minus17 second method . . . . . 22Exa 2.35 Twos complement of minus4 third method . . . . . . . 22Exa 2.36 Twos complement of minus17 third method . . . . . . 23Exa 2.37 Negative decimal number represented by 10011011 . . 24Exa 2.38 Add minus 17 to minus 30 . . . . . . . . . . . . . . . . 25Exa 2.39 Add minus 20 to 26 . . . . . . . . . . . . . . . . . . . 26Exa 2.40 Add minus 29 to 14 . . . . . . . . . . . . . . . . . . . 26

Exa 2.41 Ones complement of minus 13 . . . . . . . . . . . . . . 27Exa 2.42 Ones complement of minus 13 second method . . . . . 28Exa 2.43 Ones complement addition using 4 bits . . . . . . . . . 28Exa 2.44 Ones complement addition using 4 bits . . . . . . . . . 29Exa 2.45 Ones complement addition using 8 bits . . . . . . . . . 29Exa 2.46 Convert 1101 point 000101 to decimal . . . . . . . . . 30Exa 2.47 Convert point 375 to binary . . . . . . . . . . . . . . . 32Exa 2.48 Convert point 54545 to binary . . . . . . . . . . . . . 33Exa 2.49 Convert 38 point 21 to binary . . . . . . . . . . . . . . 34Exa 2.50 Binary addition . . . . . . . . . . . . . . . . . . . . . . 36

Exa 2.51 Binary mutiplication . . . . . . . . . . . . . . . . . . . 38Exa 3.1 Add 647 to 492 in BCD . . . . . . . . . . . . . . . . . 42Exa 3.2 Add 4318 and 7678 in BCD . . . . . . . . . . . . . . . 44Exa 3.3 Add 3 and 2 in XS3 . . . . . . . . . . . . . . . . . . . 46Exa 3.4 Add 6 and 8 in XS3 . . . . . . . . . . . . . . . . . . . 47Exa 3.5 Convert binary 1011 to Gray code . . . . . . . . . . . 48Exa 3.6 Convert binary 1001011 to Gray code . . . . . . . . . 49Exa 3.7 Convert Gray code 1011 to binary . . . . . . . . . . . 50Exa 3.8 Convert Gray code 1001011 to binary . . . . . . . . . 51Exa 3.9 Hamming code for 1011 . . . . . . . . . . . . . . . . . 52Exa 3.10 Hamming code for 0101 . . . . . . . . . . . . . . . . . 54

Exa 3.11 Correction of Hamming code 1111101 . . . . . . . . . 55Exa 4.1 Demorganize a function . . . . . . . . . . . . . . . . . 58Exa 4.2 Reduce an expression . . . . . . . . . . . . . . . . . . 58Exa 4.3 Reduce an expression . . . . . . . . . . . . . . . . . . 59Exa 4.4 Reduce a boolean expression . . . . . . . . . . . . . . 60

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Exa 4.5 Reduce a Boolean expression . . . . . . . . . . . . . . 61

Exa 6.1 Convert A plus B to minterms . . . . . . . . . . . . . 62Exa 6.2 Find minterms for A plus BC . . . . . . . . . . . . . . 62Exa 6.3 Find minterms for AB plus ACD . . . . . . . . . . . . 63Exa 6.4 Minterm designation . . . . . . . . . . . . . . . . . . . 64Exa 6.5 Minterm designation . . . . . . . . . . . . . . . . . . . 64Exa 6.6 2 variable mapping . . . . . . . . . . . . . . . . . . . . 65Exa 6.7 3 variable mapping . . . . . . . . . . . . . . . . . . . . 66Exa 6.8 Mapping an expression . . . . . . . . . . . . . . . . . 67Exa 6.9 Mapping an expression . . . . . . . . . . . . . . . . . 68Exa 6.10 4 variable mapping . . . . . . . . . . . . . . . . . . . . 69Exa 6.11 Reduce an expression by Kmap . . . . . . . . . . . . . 70

Exa 6.12 Reduce an expression using Kmap . . . . . . . . . . . 72Exa 6.13 Reduce expression by kmap . . . . . . . . . . . . . . . 74Exa 6.14.a Inputs Required . . . . . . . . . . . . . . . . . . . . . 75Exa 6.14.b Inputs required . . . . . . . . . . . . . . . . . . . . . . 75Exa 6.14.c Inputs required . . . . . . . . . . . . . . . . . . . . . . 76Exa 6.14.d Inputs required . . . . . . . . . . . . . . . . . . . . . . 76Exa 6.15 Minimise expression using mapping . . . . . . . . . . . 77Exa 6.16 Reduce using mapping . . . . . . . . . . . . . . . . . . 79Exa 6.17 Kmap POS SOP . . . . . . . . . . . . . . . . . . . . . 83Exa 6.18 Minimise expression . . . . . . . . . . . . . . . . . . . 86

Exa 6.19 Reduce kmap by POS . . . . . . . . . . . . . . . . . . 87Exa 6.20 Find minimum of expression . . . . . . . . . . . . . . 88Exa 6.24 Multiple output equation using mapping . . . . . . . . 89Exa 6.25 Multiple output equation using mapping . . . . . . . . 91Exa 6.26 Reduce by variable mapping . . . . . . . . . . . . . . 93Exa 6.27 Reduce by variable mapping . . . . . . . . . . . . . . 93Exa 6.28 Solve using 3 variable mapping . . . . . . . . . . . . . 94Exa 6.29 Reduce by mapping . . . . . . . . . . . . . . . . . . . 94Exa 6.30 Reducing expression by Kmap . . . . . . . . . . . . . 95Exa 11.1 Percentage resolution of 5bit DA converter . . . . . . . 97Exa 11.2 6 bit analog to digital converter . . . . . . . . . . . . . 97

Exa 11.3 Compute the gain of an Opamp . . . . . . . . . . . . . 98Exa 11.4 Compute the output voltage . . . . . . . . . . . . . . 99Exa 11.5 Compute output voltage . . . . . . . . . . . . . . . . . 100Exa 11.6 Resolution and Percent resolution 12bit DAconverter 101Exa 11.7 Resolution and Percent resolution 10bit ADconverter 102

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Chapter 2

Number Systems

Scilab code Exa 2.1 Convert 10111 to decimal

1 // E xampl e 2−1//2 / / B i n ar y t o D ec im a l C o n v er s i o n / /3 a = b i n 2 d e c ( ’ 1011 1 ’ )4 / / D ec im al e q u i v a l e n t o f t h e b i n a r y n umber //5 disp ( a )

6 / / a ns we r i n d e c im a l f or m //


1 // E xampl e 2−2//2 / / B i n ar y t o D ec im a l C o n v er s i o n / /3 a = b i n 2 d e c ( ’ 1011 10100 1 ’ )4 / / D ec im al e q u i v a l e n t o f t h e b i n a r y n umber //5 disp ( a )


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1 // E xampl e 2−3//2 / / B i n ar y t o D ec im a l C o n v er s i o n / /3 a = b i n 2 d e c ( ’ 1101 11 ’ )4 / / D ec im al e q u i v a l e n t o f t h e b i n a r y n umber //5 disp ( a )


Scilab code Exa 2.4 Convert 43 to binary

1 // E xampl e 2−4//2 / / D ec im al t o b i n a ry c o n v e r s i o n / /3 a = d e c 2 b i n ( 4 3 )

4 // B i n ar y e q u i v a l e n t o f t h e d e c im a l number //5 disp ( a )

6 / / a ns we r i n b i n a r y f or m //


1 // E xampl e 2−5//2 / / D ec im al t o b i n a ry c o n v e r s i o n / /3 a = d e c 2 b i n ( 2 0 0 )




1 // E xampl e 2−6//

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2 / / D ec im al t o b i n a ry c o n v e r s i o n / /

3 a = d e c 2 b i n ( 4 3 )4 // B i n ar y e q u i v a l e n t o f t h e d e c im a l number //5 disp ( a )



1 // E xampl e 2−7//

2 / / D ec im al t o b i n a ry c o n v e r s i o n / /3 a = d e c 2 b i n ( 2 0 0 )4 // B i n ar y e q u i v a l e n t o f t h e d e c im a l number //5 disp ( a )


Scilab code Exa 2.8 Add 1011 and 110

1 // E xampl e 2

−

8//2 / / B i n ar y a d d i t i o n / /3 clc

4 // c l e a r s t he c o n s o l e //5 clear

6 // c l e a r s t h e a l r e a d y e x i s t i n g v a r i a b l e s //7 x = b i n 2 d e c ( ’ 101 1 ’ )8 y = b i n 2 d e c ( ’ 110 ’ )9 / / b i n a r y t o d e ci m a l c o n v e r s i o n / /

10 z = x + y

11 / / a d d i t i o n / /

12 a = d e c 2 b i n ( z )13 / / d e ci m a l t o b i n a r y c o n v e r s i o n / /14 disp ( ’ a d di t i o n o f t h e 2 b in ar y numbers i s : ’ )15 disp ( a )


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Scilab code Exa 2.9 Add 11110 and 11

1 // E xampl e 2−9//2 / / B i n ar y a d d i t i o n / /3 clc


6 // c l e a r s t h e a l r e a d y e x i s t i n g v a r i a b l e s //

7 x = b i n 2 d e c ( ’ 1111 0 ’ )8 y = b i n 2 d e c ( ’ 1 1 ’ )9 / / b i n a r y t o d e ci m a l c o n v e r s i o n / /

10 z = x + y

11 / / a d d i t i o n / /12 a = d e c 2 b i n ( z )

13 / / d e ci m a l t o b i n a r y c o n v e r s i o n / /14 disp ( ’ a d di t i o n o f t h e 2 b in ar y numbers i s : ’ )15 disp ( a )


Scilab code Exa 2.10 Subtract one from 100

1 // E xampl e 2−10//2 / / B i n ar y S u b t r a c t i o n / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = b i n 2 d e c ( ’ 100 ’ )

8 y = b i n 2 d e c ( ’ 1 ’ )9 / / b i n a r y t o d e ci m a l c o n v e r s i o n / /

10 z = x - y

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11 / / s u b t r a c t i o n / /

12 a = d e c 2 b i n ( z )13 / / d e ci m a l t o b i n a r y c o n v e r s i o n / /14 disp ( ’ s u b t r a c t i o n o f two b i na r y numbers i s : ’ )15 disp ( a )


Scilab code Exa 2.11 Multiply 1011 by 101

1 // E xampl e 2−

11//2 // B i na ry m u l t i p l i c a t i o n //3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = b i n 2 d e c ( ’ 101 1 ’ )8 y = b i n 2 d e c ( ’ 101 ’ )9 / / b i n a r y t o d e ci m a l c o n v e r s i o n / /

10 z = x * y ;

11 / / m u l t i p l i c a t i o n / /

12 a = d e c 2 b i n ( z )13 / / d e ci m a l t o b i n a r y c o n v e r s i o n / /14 disp ( ’ m u l t i p l i c a t i o n o f two b in ar y numbers i s : ’ )15 disp ( a )


Scilab code Exa 2.12 Multiply 11010 by 11011

1 // E xampl e 2−

12//2 // B i na ry m u l t i p l i c a t i o n //3 clc


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6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //

7 x = b i n 2 d e c ( ’ 1101 0 ’ )8 y = b i n 2 d e c ( ’ 1101 1 ’ )9 / / b i n a r y t o d e ci m a l c o n v e r s i o n / /

10 z = x * y ;

11 / / m u l t i p l i c a t i o n / /12 a = d e c 2 b i n ( z )

13 / / d e ci m a l t o b i n a r y c o n v e r s i o n / /14 disp ( ’ m u l t i p l i c a t i o n o f two b in ar y numbers i s : ’ )15 disp ( a )


Scilab code Exa 2.13 Divide 110110 by 101

1 // E xampl e 2−13//2 / / B in ar y D i v i s i o n //3 x = b i n 2 d e c ( ’ 1101 10 ’ )4 y = b i n 2 d e c ( ’ 101 ’ )5 r = modul o ( x , y )

6 / / f i n d i n g t h e r e ma i n de r / /

7 z = x / y8 q = floor ( z )

9 / / f i n d i n g t h e q u o t i e n t //10 q u o = d e c 2 b i n ( q )

11 r e m = d e c 2 b i n ( r )

12 / / d e ci m a l t o b i n a r y c o n v e r s i o n s / /13 disp ( ’ t h e q u o t ie n t i s : ’ )14 disp ( q u o )

15 disp ( ’ t h e r e ma in de r i s : ’ )16 disp ( r e m )

17 / / a n sw e rs i n b i n a ry f or m //

Scilab code Exa 2.14 Convert 1010111010 to hexadecimal

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1 // E xampl e 2−14//

2 / / b i n a r y t o h e xa d e ci m a l c o n v e r s i o n //3 x = b i n 2 d e c ( ’ 1010 11101 0 ’ )4 / / d e ci m a l e q u i v a l e n t o f t h e b i n a ry number //5 a = dec2hex ( x )

6 / / Hex e q u i v a l e n t o f t h e d e ci m a l number //7 disp ( a )

8 / / a n sw er i n h e xa d e ci m a l f or m //


1 // E xampl e 2−15//2 / / b i n a r y t o h e xa d e ci m a l c o n v e r s i o n //3 x = b i n 2 d e c ( ’ 1 1 0 1 1 1 1 0 1 0 1 1 1 0 ’ )4 / / d e ci m a l e q u i v a l e n t o f t h e b i n a ry number //5 a = dec2hex ( x )

6 / / Hex e q u i v a l e n t o f t h e d e ci m a l number //7 disp ( a )


Scilab code Exa 2.16 Convert 4A8C to binary

1 // E xampl e 2−16//2 / / H ex ad ec im al t o b i n a r y c o n v e r s i o n //3 x = hex2dec ( ’ 4A8C ’ )4 / / d e ci m a l c o n v e r s i o n o f t h e h e xa d ec i ma l number //5 a = d e c 2 b i n ( x )

6 // B i n ar y e q u i v a l e n t o f t h e d e c im a l number //

7 disp ( a )8 / / a ns we r i n b i n a r y f or m //

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Scilab code Exa 2.17 Convert FACE to binary

1 // E xampl e 2−17//2 / / H ex ad ec im al t o b i n a r y c o n v e r s i o n //3 x = hex2dec ( ’FACE ’ )4 / / d e ci m a l c o n v e r s i o n o f t h e h e xa d ec i ma l number //5 a = d e c 2 b i n ( x )



Scilab code Exa 2.18 Convert 2C9 to decimal

1 // E xampl e 2−18//2 / / H ex ad ec im al t o d e ci m a l c o n v e r s i o n / /3 a = hex2dec ( ’ 2C9 ’ )4 / / d e ci m a l e q u i v a l e n t o f t h e h e xa d ec i ma l number //5 disp ( a )


Scilab code Exa 2.19 Convert EB4A to decimal

1 // E xampl e 2−19//2 / / H ex ad ec im al t o d e ci m a l c o n v e r s i o n / /3 a = hex2dec ( ’EB4A ’ )4 / / d e ci m a l e q u i v a l e n t o f t h e h e xa d ec i ma l number //5 disp ( a )



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1 // E xampl e 2−20//

2 / / D ec im al t o h e xa d ec i ma l c o n v e r s i o n / /3 a = dec2hex (423)4 / / h e xa d e ci m a l e q u i v a l e n t o f t h e d e c im a l number //5 disp ( a )



1 // E xampl e 2−

21//2 / / D ec im al t o h e xa d ec i ma l c o n v e r s i o n / /3 a = dec2hex (72905)

4 / / h e xa d e ci m a l e q u i v a l e n t o f t h e d e c im a l number //5 disp ( a )


Scilab code Exa 2.22 Add 1A8 and 67B

1 // E xampl e 2−22//2 / / H e xa d ec i ma l a d d i t i o n / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = hex2dec ( ’ 1A8 ’ )8 y = hex2dec ( ’ 6 7B ’ )9 / / D ec im al c o n v e r s i o n o f t h e h e xa d ec i ma l nu mbers / /

10 z = x + y

11 / / a d d i t i o n / /12 a = dec2hex ( z )

13 / / d e ci m a l t o h e xa d ec i ma l c o n v e r s i o n / /14 disp ( ’ a d d i ti o n o f t he 2 h ex ad ec im al numbers i s ’ )15 disp ( a )

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Scilab code Exa 2.23 Add ACEF1 and 16B7D

1 // E xampl e 2−23//2 / / H e xa d ec i ma l a d d i t i o n / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = hex2dec ( ’ ACEF1 ’ )8 y = hex2dec ( ’ 16B7D ’ )9 / / D ec im al c o n v e r s i o n o f t h e h e xa d ec i ma l nu mbers / /

10 z = x + y

11 / / a d d i t i o n / /12 a = dec2hex ( z )

13 / / d e ci m a l t o h e xa d ec i ma l c o n v e r s i o n / /14 disp ( ’ a d d i ti o n o f t he 2 h ex ad ec im al numbers i s ’ )15 disp ( a )


Scilab code Exa 2.24 Subtract 3A8 from 1273

1 // E xampl e 2−24//2 / / H e xa d ec i ma l S u b t r a c t i o n / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = hex2dec ( ’ 127 3 ’ )8 y = hex2dec ( ’ 3A8 ’ )9 / / D ec im al c o n v e r s i o n o f t h e h e xa d ec i ma l nu mbers / /

10 z = x - y

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11 / / a d d i t i o n / /

12 a = dec2hex ( z )13 / / d e ci m a l t o h e xa d ec i ma l c o n v e r s i o n / /14 disp ( ’ a d d i ti o n o f t he 2 h ex ad ec im al numbers i s ’ )15 disp ( a )


Scilab code Exa 2.25 Multiply 1A3 by 89

1 // E xampl e 6−

25//2 / / S o l v e m u l t i p l e o ut p ut e q u a t io n u s i n g mapping / /3 clc

4 / / c l e a r s t h e window / /5 clear

6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = hex2dec ( ’ 1A3 ’ )8 y = hex2dec ( ’ 8 9 ’ )9 / / D ec im al c o n v e r s i o n o f t h e h e xa d ec i ma l nu mbers / /

10 z = x * y

11 / / m u l t i p l i c a t i o n / /

12 a = dec2hex ( z )13 / / d e ci m a l t o h e xa d ec i ma l c o n v e r s i o n / /14 disp ( ’ m u l t i p l i c a t i o n o f t he 2 h ex ad ec im al numbers

i s ’ )15 disp ( a )


Scilab code Exa 2.26 Divide 1EC87 by A5

1 // E xampl e 2−26//2 / / H e xa d ec i ma l D i v i s i o n / /3 x = hex2dec ( ’ 1EC87 ’ )4 y = hex2dec ( ’ A5 ’ )

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5 r = modul o ( x , y )

6 / / f i n d i n g t h e r e ma i n de r / /7 z = x / y8 q = floor ( z )

9 / / f i n d i n g t h e q u o t i e n t //10 q u o = dec2hex ( q )

11 r e m = dec2hex ( r )

12 / / d e ci m a l t o b i n a r y c o n v e r s i o n s / /13 disp ( ’ t h e q u o t ie n t i s : ’ )14 disp ( q u o )

15 disp ( ’ t h e r e ma in de r i s : ’ )16 disp ( r e m )


Scilab code Exa 2.27 Convert 11111011110101 to octal

1 // E xampl e 2−27//2 // B i na ry t o o c t a l c o n v e r si o n //3 x = b i n 2 d e c ( ’ 1 1 1 1 1 0 1 1 1 1 0 1 0 1 ’ )4 / / d e ci m a l e q u i v a l e n t o f t h e b i n a ry number //

5 a = d e c 2 o c t ( x )6 // o c t a l e q u i v a l e n t o f t he d ec i ma l number //7 disp ( a )

8 / / an sw er i n o c t a l fo rm / /

Scilab code Exa 2.28 Convert 1011110100011000111 to octal

1 // E xampl e 2−28//

2 // B i na ry t o o c t a l c o n v e r si o n //3 x = b i n 2 d e c ( ’ 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 ’ )4 / / d e ci m a l e q u i v a l e n t o f t h e b i n a ry number //5 a = d e c 2 o c t ( x )

6 // o c t a l e q u i v a l e n t o f t he d ec i ma l number //

18


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7 disp ( a )

8 / / an sw er i n o c t a l fo rm / /

Scilab code Exa 2.29 Convert octal number 3674 to binary

1 // E xampl e 2−29//2 // o c t a l t o b i na r y c o n v e r si o n //3 x = o c t 2 d e c ( ’ 367 4 ’ )4 // d ec i ma l e q u i v a l e n t o f t he o c t a l number //

5 a = d e c 2 b i n ( x )6 / / b i n a r y e q u i v a l e n t o f t h e d e c im a l number //7 disp ( a )


Scilab code Exa 2.30 Minus 5 in twos complement form

1 // E xampl e 2−30//

2 // −

5 i n t w o s complement fo rm / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = 2 ^ 8

8 / / S m a l l e s t n i n e b i t number //9 y =5

10 z = x - y

11 / / s u b t r a c t i o n / /12 a = d e c 2 b i n ( z )

13 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //14 disp ( ’ −5 i n t w o s complement form i s ’ )15 disp ( a )


19


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Scilab code Exa 2.31 12 bit twos complement

1 // E xampl e 2−31//2 // −4 ,−15 ,−17 i n t w o s complement fo rm / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = 2 ^ 1 2

8 / / S m a l l e s t n i n e b i t number //9 p =4

10 q = 1 5

11 r = 1 7

12 u = x - p

13 v = x - q

14 w = x - r

15 / / s u b t r a c t i o n / /16 a = d e c 2 b i n ( u )

17 b = d e c 2 b i n ( v )

18 c = d e c 2 b i n ( w )19 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //20 disp ( ’ −4 i n t w o s complement form i s ’ )21 disp ( a )

22 disp ( ’ −15 i n t w o s complement form i s ’ )23 disp ( b )

24 disp ( ’ −17 i n t w o s complement form i s ’ )25 disp ( c )


Scilab code Exa 2.32 16 bit twos complement

1 // E xampl e 2−32//

20


22/104

2 // −16000 i n t w o s co mpl em en t f or m //

3 clc4 // c l e a r s t he c o n s o l e //5 clear

6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = 2 ^ 1 6

8 / / S m a l l e s t n i n e b i t number //9 y = 1 6 0 0 0

10 z = x - y

11 / / s u b t r a c t i o n / /12 a = d e c 2 b i n ( z )

13 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //

14 disp ( ’ −

16000 i n t w o s complement fo rm i s ’ )15 disp ( a )


Scilab code Exa 2.33 Twos complement of minus4 second method

1 // E xampl e 2−33//2 // −4 i n t w o s c om pl em en t f or m by s e co n d method / /

3 clc4 / / c l e a r s t h e window / /5 clear

6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = b i t c m p ( 4 , 8 )

8 / / c om pl em en t o f t h e d e c im a l number 4 ( 8 b i tr e p r e s e n t a t i o n ) //

9 y =1

10 z = x + y

11 / / 1 i s a dded t o t h e co mp lem en t //

12 a = d e c 2 b i n ( z )13 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //14 disp ( ’ −4 i n t w o s complement form i s : ’ )15 disp ( a )

16 // r e s u l t i s d i s p la y e d //

21


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Scilab code Exa 2.34 Twos complement of minus17 second method

1 // E xampl e 2−34//2 // −17 i n t w o s co mp le men t f or m by s e co n d method / /3 clc



7 x = b i t c m p ( 1 7 , 8 )8 / / c om pl em en t o f t h e d e c im a l number 1 7 (8 b i t

r e p r e s e n t a t i o n ) //9 y =1

10 z = x + y

11 / / 1 i s a dde d t o t h e co mp lem en t //12 a = d e c 2 b i n ( z )

13 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //14 disp ( ’ −17 i n t w o s complement form i s : ’ )15 disp ( a )


Scilab code Exa 2.35 Twos complement of minus4 third method

1 // E xampl e 2−35//2 //−4 i n two ’ s c om pl em en t by t h i r d method / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 a = 0 0 0 0 0 1 0 0

8 c =0

9 z =0

22


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10 for i =1: 8

11 x ( i ) = modulo ( a , 1 0 )12 a = a / 1 0

13 a = floor ( a )

14 end

15 for i =1: 8

16 if c >1 then

17 break

18 end

19 if x ( i ) = = 1 then

20 for k = i +1 : 8

21 x ( k ) = b i t c m p ( x ( k ) , 1 )

22 c = c + 123 end

24 end

25 end

26 for i =1: 8

27 z = z + x ( i ) * 1 0 ^ ( i - 1 )

28 end

29 disp ( ’−4 i n t wo s complement i s : ’ )30 disp ( z )

31 // a ns we r i s d i s p l a y e d //

Scilab code Exa 2.36 Twos complement of minus17 third method

1 // E xampl e 2−36//2 //−17 i n two ’ s c om pl em en t by t h i r d m et ho d / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 a = 0 0 0 1 0 0 0 18 c =0

9 z =0

10 for i =1: 8

23


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11 x ( i ) = modulo ( a , 1 0 )

12 a = a / 1 013 a = floor ( a )

14 end

15 for i =1: 8

16 if c >1 then

17 break

18 end

19 if x ( i ) = = 1 then

20 for k = i +1 : 8

21 x ( k ) = b i t c m p ( x ( k ) , 1 )

22 c = c + 1

23 end24 end

25 end

26 for i =1: 8

27 z = z + x ( i ) * 1 0 ^ ( i - 1 )

28 end

29 disp ( ’ −17 i n t wo s co mp le men t i s : ’ )30 disp ( z )

31 // a ns we r i s d i s p l a y e d //

Scilab code Exa 2.37 Negative decimal number represented by 10011011

1 // E xampl e 2−37//2 / / n e g at i v e d ec im al r e p r e s e n t a t i o n o f 1 00 11 01 1/ /3 clc



7 b = b i n 2 d e c ( ’ 10011 011 ’ )8 x = b i t c m p ( b , 8 )9 / / c om pl em en t o f t h e d e c im a l number 1 7 (8 b i t

r e p r e s e n t a t i o n ) //10 y =1

24


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11 z = x + y

12 / / 1 i s a dde d t o t h e co mp lem en t //13 a = d e c 2 b i n ( z )14 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //15 z = z * ( - 1 )

16 disp ( ’ t he n e g at i v e v al ue t ha t 1 00 11 01 1 r e p r e s e n t si s : ’ )

17 disp ( z )


Scilab code Exa 2.38 Add minus 17 to minus 30

1 // E xampl e 2−38//2 //add −17 t o −30//3 clc


6 // c l e a r s a l l e x i s i t i n g v a r i a b l e s //7 x = b i t c m p ( 1 7 , 8 )

8 y = b i t c m p ( 3 0 , 8 )

9 / / c om pl em en t o f t h e d e c i m a l n um be rs 1 7 a nd 3 0/ /10 z =1

11 u = x + z

12 v = y + z

13 / / 1 i s a dde d t o t h e c om pl em en ts / /14 w = u + v

15 a = d e c 2 b i n ( w )

16 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //17 disp ( ’ b i n a r y f or m o f number o b t a i ne d by a d di ng −17

t o −30 ’ )

18 disp ( a )19 // r e s u l t i s d i s p la y e d //20 disp ( ’ t he msb i s d i s c a r d e d , s o e i g h t b i t

r e p r e s e n t a t i o n i s t he an s we r i n b in ar y form ’ )21 a = d e c 2 b i n ( w - ( 2 ^ 8 ) )

25


27/104

22 disp ( a )

23 // f i n a l r e s u l t i s d i sp l ay e d //

Scilab code Exa 2.39 Add minus 20 to 26

1 // E xampl e 2−39//2 //add −20 t o 2 6/ /3 clc

4 // c l e a r s t he c o n s o l e //

5 clear6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = b i t c m p ( 2 0 , 8 )

8 / / f i n d s c om pl em en t o f 2 9 //9 y =1

10 u = x + y

11 / / 1 i s a dde d t o t h e co mp lem en t //12 v = 2 6

13 w = u + v

14 a = d e c 2 b i n ( w )

15 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //

16 disp ( ’ b i na r y form o f t he number o b ta i ne d by a dd in g−20 t o 26 ’ )

17 disp ( a )

18 // r e s u l t i s d i s p la y e d //19 disp ( ’ t he msb i s d i s c a r d e d , s o e i g h t b i t

r e p r e s e n t a t i o n i s t he an s we r i n b in ar y form ’ )20 a = d e c 2 b i n ( w - ( 2 ^ 8 ) )

21 disp ( a )

22 // f i n a l r e s u l t i s d i sp l ay e d //

Scilab code Exa 2.40 Add minus 29 to 14

1 // E xampl e 2−40//

26


28/104

2 //add −29 t o 1 4/ /


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = b i t c m p ( 2 9 , 8 )

8 / / f i n d s c om pl em en t o f 2 9 //9 y =1

10 u = x + y

11 / / 1 i s a dde d t o t h e co mp lem en t //12 v = 1 4

13 w = u + v

14 a = d e c 2 b i n ( w )15 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //16 disp ( ’ b i na r y form o f t he number o b ta i ne d by a dd in g

−29 t o 14 ’ )17 disp ( a )


Scilab code Exa 2.41 Ones complement of minus 13

1 // E xampl e 2−41//2 / / o ne ’ s c om pl em en t f or m o f −13//3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 x = b i t c m p ( 1 3 , 8 )

8 / / c o mp le me nt o f 1 3 //9 a = d e c 2 b i n ( x )

10 / / b i n a r y c o n v e r s i o n o f t h e d e c im a l number //11 disp ( ’ o n es c om pl em en t f or m o f −13 ’ )12 disp ( a )


27


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Scilab code Exa 2.42 Ones complement of minus 13 second method

1 // E xampl e 2−42//2 / / o n e s c om pl em en t o f −13 b y 2 n d m et ho d / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 a = b i t c m p ( 0 , 8 )

8 / / d e ci m a l e q u i v a l e n t o f 1 1 11 11 1 1/ /9 b = 1 3

10 c = a - b

11 / / s u b t r a c t i n g 13 from d e ci m al e q u i v a l e n t o f 1 1 1 1 1 1 1 1 / /

12 z = d e c 2 b i n ( c )

13 disp ( ’ o n e s c om pl em en t o f −13 i s : ’ )14 disp ( z )


Scilab code Exa 2.43 Ones complement addition using 4 bits

1 // E xampl e 2−43//2 //add −3 t o −2 i n one ’ s c om pl em ent u s i n g 4 b i t s / /3 clc


6 // c l e a r s a l l t h e e x i s t i n g v a r i a b l e s //

7 x = b i t c m p ( 3 , 4 )8 y = b i t c m p ( 2 , 4 )

9 / / c o mp le me nt o f t h e d e c i m a l number 2 //10 z = x + y + 1

11 / / c a r r y i s a dd ed / /

28


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12 a = d e c 2 b i n ( z )

13 / / b i n a r y c o n v e r s i o n / /14 disp ( ’ b i n a r y f or m o f t h e number o b t a i n ed by a d di n g−3 t o −2 ’ )

15 disp ( a )

16 // r e s u l t i s d i s p la y e d //17 disp ( ’ msb i s d is ca rd ed , 4 b i t r e p r e s e n t a t i o n i s t he

a ns we r i n b i n a r y f or m ’ )18 a = d e c 2 b i n ( z - ( 2 ^ 4 ) )

19 disp ( a )

20 // F i na l r e s u l t i s d i s p l a y e d //


1 // E xampl e 2−44//2 //add −3 t o 2 i n one ’ s complement u s i ng 4 b i t s //3 clc


6 // c l e a r s a l l t h e e x i s t i n g v a r i a b l e s //

7 x =28 y = b i t c m p ( 3 , 4 )

9 / / c o mp le me nt o f t h e d e c i m a l number 2 //10 z = x + y

11 a = d e c 2 b i n ( z )

12 / / b i n a r y c o n v e r s i o n / /13 disp ( ’ b i n a r y f or m o f t h e number o b t a i n ed by a d di n g

−3 t o 2 ’ )14 disp ( a )



29


31/104

1 // E xampl e 2−45//

2 / / add 3 t o −

2 i n one ’ s co mp le men t u s i n g 8 b i t s / /3 clc4 / / c l e a r s t h e window / /5 clear

6 // c l e a r s a l l t h e e x i s t i n g v a r i a b l e s //7 x =3

8 y = b i t c m p ( 2 , 8 )

9 / / c o mp le me nt o f t h e d e c i m a l number 2 //10 z = x + y + 1

11 / / c a r r y i s a dd ed / /12 a = d e c 2 b i n ( z )

13 / / b i n a r y c o n v e r s i o n / /14 disp ( ’ b i n a r y f or m o f t h e number o b t a i n ed by a d di n g 3

t o −2 ’ )15 disp ( a )

16 // r e s u l t i s d i s p la y e d //17 disp ( ’ msb i s d is ca rd ed , 8 b i t r e p r e s e n t a t i o n i s t he

a ns we r i n b i n a r y f or m ’ )18 a = d e c 2 b i n ( z - ( 2 ^ 8 ) )

19 disp ( a )

20 // F i na l r e s u l t i s d i s p l a y e d //

Scilab code Exa 2.46 Convert 1101 point 000101 to decimal

1 // E xampl e 2−46//2 / / C o n v er s i o n t o d e c i m a l / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 p =18 q =1

9 z =0

10 b =0

30


32/104

11 w =0

12 f =013 // i n i t i a l i s i n g / /14 / / b i n=i n p u t ( e n t e r t h e b i n a r y number t o be c o n v e rt e d

t o i t s d e ci m al fo rm ) / /15 // a c c e p ti n g t he i n pu t from t he u s e r //16 b i n = 1 1 0 1 . 0 0 0 1 0 1

17 d = modul o ( b i n , 1 )

18 / / s e p a r at i n g t he d ec im al p ar t from t he i n t e g e r p ar t//

19 d = d * 1 0 ^ 1 0

20 a = floor ( b i n )

21 / / r em o vi n g t h e d e c i m a l p a r t / /22 while ( a > 0 )

23 / / l oo p t o e n t e r t h e b in ar y b i t s o f t he i n t e g e r p ar ti n t o a m a tr i x / /

24 r = modul o ( a , 1 0 )

25 b ( 1 , q ) = r

26 a = a / 1 0

27 a = floor ( a )

28 q = q + 1

29 end

30 for m = 1: q - 1

31 / / m u l t i pl y i n g e a c h b i t o f t h e i n t e g e r p ar t w i t h i t sc o r r e sp o n di n g p o s i t i o n a l v al ue and a dd in g //

32 c = m - 1

33 f = f + b ( 1 , m ) * ( 2 ^ c )

34 end

35 while ( d > 0 )

36 / / l oo p t o t ak e t he b i t s o f t he d ec im al p ar t i n t o amat r i x //

37 e = modul o ( d , 2 )

38 w ( 1 , p ) = e

39 d = d / 1 040 d = floor ( d )

41 p = p + 1

42 end

43 for n = 1: p - 1

31


33/104

44 / / m u l t i p l y i n g e a ch b i t w i th i t s c o r r e sp o n di n g

p o s i t i o n a l v al ue and a dd in g //45 z = z + w ( 1 , n ) * ( 0 . 5 ) ^ ( 1 1 - n )46 end

47 z = z * 1 0 0 0 0

48 z = round ( z )

49 // r ou nd in g o f f t o 4 d e ci m al p l a c e s //50 z = z / 1 0 0 0 0

51 x = f + z

52 disp ( ’ t he d e ci m al e q u i v a l e n t o f t he b i na r y number i s: ’ )

53 disp ( x )


Scilab code Exa 2.47 Convert point 375 to binary

1 // E xampl e 2−47//2 / / C o nv e rs i o n o f d e ci m a l t o b i n a r y / /3 clc


5 clear6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 q =0

8 b =0

9 s =0

10 // i n i t i a l i s i n g / /11 / / a=i n p u t ( e n t e r t h e d e c i m a l number t o b e c o n v e r t e d

t o i t s b i n ar y form )12 / / t a k i n g i n p u t f ro m t h e u s e r / /13 a = 0 . 3 7 5

14 d = modul o ( a , 1 )15 // s e p a r a t i n g t he d ec i ma l p a rt fro m t he i n t e g e r //16 a = floor ( a )


32


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19 // i n t e g e r p ar t c on v e rt e d t o e q u i v a l e n t b i n ar y form //

20 x = modul o ( a , 2 )21 b = b + ( 1 0 ^ q ) * x

22 a = a / 2

23 a = floor ( a )

24 q = q + 1

25 end

26 for i = 1: 1 0

27 / / t a ki n g v a l ue s a f t e r t he d ec im al p ar t andc o n ve r t i n g t o e q u i v a l e n t b i n a ry form //

28 d = d * 2

29 q = floor ( d )

30 s = s + q / ( 1 0 ^ i )31 if d > = 1 then

32 d = d - 1

33 end

34 end

35 k = b + s

36 disp ( ’ t he d e ci m al number i n b i na r y fo rm i s : ’ )37 disp ( k )


Scilab code Exa 2.48 Convert point 54545 to binary




7 q =08 b =0

9 s =0


33


35/104

t o i t s b i n ar y form )

12 / / t a k i n g i n p u t f ro m t h e u s e r / /13 a = 0 . 5 4 5 4 514 d = modul o ( a , 1 )

15 // s e p a r a t i n g t he d ec i ma l p a rt fro m t he i n t e g e r //16 a = floor ( a )


19 // i n t e g e r p ar t c on v e rt e d t o e q u i v a l e n t b i n ar y form //20 x = modul o ( a , 2 )

21 b = b + ( 1 0 ^ q ) * x

22 a = a / 2

23 a = floor ( a )24 q = q + 1

25 end

26 for i = 1: 1 0


28 d = d * 2

29 q = floor ( d )

30 s = s + q / ( 1 0 ^ i )

31 if d > = 1 then

32 d = d - 1

33 end

34 end

35 k = b + s

36 disp ( ’ t he d e ci m al number i n b i na r y fo rm i s : ’ )37 disp ( k )


Scilab code Exa 2.49 Convert 38 point 21 to binary


34


36/104


5 clear6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 q =0

8 b =0

9 s =0


t o i t s b i n ar y form )12 / / t a k i n g i n p u t f ro m t h e u s e r / /13 a = 3 8 . 2 1

14 d = modul o ( a , 1 )




21 b = b + ( 1 0 ^ q ) * x

22 a = a / 2

23 a = floor ( a )

24 q = q + 1

25 end

26 for i = 1: 1 0


28 d = d * 2

29 q = floor ( d )

30 s = s + q / ( 1 0 ^ i )

31 if d > = 1 then

32 d = d - 1

33 end

34 end

35 k = b + s36 disp ( ’ t h e i n t e g e r p ar t o f t h e b in ar y for m i s : ’ )37 disp ( b )

38 disp ( ’ t h e f r a c t i o n a l p ar t o f t h e b in ar y form i s : ’ )39 disp ( s )

35


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Scilab code Exa 2.50 Binary addition

1 // E xampl e 2−50//2 / / a d d i t i o n o f b i n a r y n umb ers / /3 // t h i s program r e q u i r e s f u n c t i o n s b i n ar y 2 de c im a l . s c i

and d e c i m a l 2 b i n a r y . s c i / /4 clc


7 // c l e a r s a l l e x i s t i n g v a r i a b l e s //8 function x = b i n a r y 2 d e c i m a l ( b i n )

9 p =1

10 q =1

11 z =0

12 b =0

13 w =0

14 f =0

15 // i n i t i a l i s i n g / /

16 d = modul o ( b i n , 1 )17 / / s e p a r at i n g t he d ec im al p ar t from t he i n t e g e r p ar t

//18 d = d * 1 0 ^ 1 0

19 a = floor ( b i n )


22 / / l oo p t o e n t e r t h e b in ar y b i t s o f t he i n t e g e r p ar ti n t o a m at ri x //

23 r = modul o ( a , 1 0 )

24 b ( 1 , q ) = r25 a = a / 1 0

26 a = floor ( a )

27 q = q + 1

28 end

36


38/104

29 for m = 1: q - 1

30 / / m u l t i pl y i n g e a c h b i t o f t h e i n t e g e r p ar t w i t h i t sc o r r e sp o n di n g p o s i t i o n a l v al ue and a dd in g //31 c = m - 1

32 f = f + b ( 1 , m ) * ( 2 ^ c )

33 end

34 while ( d > 0 )


36 e = modul o ( d , 2 )

37 w ( 1 , p ) = e

38 d = d / 1 0

39 d = floor ( d )40 p = p + 1

41 end

42 for n = 1: p - 1

43 / / m u l t i p l y i n g e a ch b i t w i th i t s c o r r e sp o n di n gp o s i t i o n a l v al ue and a dd in g //

44 z = z + w ( 1 , n ) * ( 0 . 5 ) ^ ( 1 1 - n )

45 end

46 z = z * 1 0 0 0 0

47 z = round ( z )


50 x = f + z

51 e n d f u n c t i o n

52 function y = d e c i m a l 2 b i n a r y ( a )

53 q =0

54 b =0

55 s =0

56 // i n i t i a l i s i n g / /57 d = modul o ( a , 1 )

58 // s e p a r a t i n g t he d ec i ma l p a rt fro m t he i n t e g e r //

59 a = floor ( a )60 / / r em o vi n g t h e d e c i m a l p a r t / /61 while ( a > 0 )


37


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64 b = b + ( 1 0 ^ q ) * x

65 a = a / 266 a = floor ( a )

67 q = q + 1

68 end

69 for i = 1: 1 0


71 d = d * 2

72 q = floor ( d )

73 s = s + q / ( 1 0 ^ i )

74 if d > = 1 then

75 d = d - 176 end

77 end

78 y = b + s


80 x = b i n a r y 2 d e c i m a l ( 1 1 . 0 1 1 )

81 y = b i n a r y 2 d e c i m a l ( 1 0 . 0 0 1 )

82 z = x + y

83 a = d e c i m a l 2 b i n a r y ( z )

84 disp ( ’ t he a d d i ti o n o f t he b i n ar y numbers i s : ’ )85 disp ( a )


Scilab code Exa 2.51 Binary mutiplication

1 // E xampl e 2−51//2 // m u l t i p l i c a t i o n o f b i na r y numbers //3 // t h i s program r e q u i r e s f u n c t i o n s b i n ar y 2 de c im a l . s c i

and d e c i m a l 2 b i n a r y . s c i / /4 clc5 / / c l e a r s t h e window / /6 clear


38


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8 function x = b i n a r y 2 d e c i m a l ( b i n )

9 p =110 q =1

11 z =0

12 b =0

13 w =0

14 f =0

15 // i n i t i a l i s i n g / /16 d = modul o ( b i n , 1 )

17 / / s e p a r at i n g t he d ec im al p ar t from t he i n t e g e r p ar t//

18 d = d * 1 0 ^ 1 0

19 a = floor ( b i n )20 / / r em o vi n g t h e d e c i m a l p a r t / /21 while ( a > 0 )

22 / / l oo p t o e n t e r t h e b in ar y b i t s o f t he i n t e g e r p ar ti n t o a m at ri x //

23 r = modul o ( a , 1 0 )

24 b ( 1 , q ) = r

25 a = a / 1 0

26 a = floor ( a )

27 q = q + 1

28 end

29 for m = 1: q - 1

30 / / m u l t i pl y i n g e a c h b i t o f t h e i n t e g e r p ar t w i t h i t sc o r r e sp o n di n g p o s i t i o n a l v al ue and a dd in g //

31 c = m - 1

32 f = f + b ( 1 , m ) * ( 2 ^ c )

33 end

34 while ( d > 0 )


36 e = modul o ( d , 2 )

37 w ( 1 , p ) = e38 d = d / 1 0

39 d = floor ( d )

40 p = p + 1

41 end

39


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42 for n = 1: p - 1

43 / / m u l t i p l y i n g e a ch b i t w i th i t s c o r r e sp o n di n gp o s i t i o n a l v al ue and a dd in g //44 z = z + w ( 1 , n ) * ( 0 . 5 ) ^ ( 1 1 - n )

45 end

46 z = z * 1 0 0 0 0

47 z = round ( z )


50 x = f + z


52 function y = d e c i m a l 2 b i n a r y ( a )

53 q =054 b =0

55 s =0

56 // i n i t i a l i s i n g / /57 d = modul o ( a , 1 )




64 b = b + ( 1 0 ^ q ) * x

65 a = a / 2

66 a = floor ( a )

67 q = q + 1

68 end

69 for i = 1: 1 0


71 d = d * 2

72 q = floor ( d )

73 s = s + q / ( 1 0 ^ i )74 if d > = 1 then

75 d = d - 1

76 end

77 end

40


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78 y = b + s

79 e n d f u n c t i o n80 x = b i n a r y 2 d e c i m a l ( 1 0 . 0 0 1 )

81 y = b i n a r y 2 d e c i m a l ( 0 . 1 1 )

82 z = x * y

83 a = d e c i m a l 2 b i n a r y ( z )

84 disp ( ’ t he m u l t i p l i c a t i o n o f t he b i n a ry numbers i s : ’)

85 disp ( a )


41


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Chapter 3

Binary Codes

Scilab code Exa 3.1 Add 647 to 492 in BCD

1 // E xampl e 3−1//2 //BCD ad di t i on //3 clc



7 a = 6 4 78 b = 4 9 2

9 for i =1: 3

10 x ( i ) = modulo ( a , 1 0 )

11 a = a / 1 0

12 a = floor ( a )

13 y ( i ) = modulo ( b , 1 0 )

14 b = b / 1 0

15 b = floor ( b )

16 end

17 d = x ( 1 ) + y ( 1 )18 d b = d e c 2 b i n ( d )

19 if d >9 then

20 d b = d e c 2 b i n ( d + 6 )

21 d b = d e c 2 b i n ( b i n 2 d e c ( d b ) - b i n 2 d e c ( ’ 1000 0 ’ ) )

42


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22 end

23 e = x ( 2 ) + y ( 2 )24 e b = d e c 2 b i n ( e )

25 if d >9 then

26 e b = d e c 2 b i n ( e + 1 )

27 e = e + 1

28 end

29 if e >9

30 e b = d e c 2 b i n ( e + 6 )

31 e b = d e c 2 b i n ( b i n 2 d e c ( e b ) - b i n 2 d e c ( ’ 1000 0 ’ ) )32 end

33 f = x ( 3 ) + y ( 3 )

34 f b = d e c 2 b i n ( f )35 if e >9 then

36 f b = d e c 2 b i n ( f + 1 )

37 f = f + 1

38 end

39 if f >9

40 f b = d e c 2 b i n ( f + 6 )

41 f b = d e c 2 b i n ( b i n 2 d e c ( f b ) - b i n 2 d e c ( ’ 1000 0 ’ ) )42 d c ( 4 ) = 1

43 end

44 d c ( 1 ) = b i n 2 d e c ( d b )

45 d c ( 2 ) = b i n 2 d e c ( e b )

46 d c ( 3 ) = b i n 2 d e c ( f b )

47 z =0

48 for i =1 : 4

49 z = z + d c ( i ) * ( 1 0 ^ ( i - 1 ) )

50 end

51 disp ( z )

52 disp ( ’ e q u i v a l e n t b i n a r y fo rm ’ )53 p = strcat ( d e c 2 b i n ( d c ( 4 ) , 1 ) + d e c 2 b i n ( d c ( 3 ) , 4 ) + d e c 2 b i n (

d c ( 2 ) , 4 ) + d e c 2 b i n ( d c ( 1 ) , 4 ) )

54 disp ( p )55 // a ns we r i s d i s p l a y e d //

43


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Scilab code Exa 3.2 Add 4318 and 7678 in BCD

1 // E xampl e 3−2//2 //BCD ad di t i on //3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 a = 4 3 1 8

8 b = 7 6 7 8

9 for i =1: 4

10 x ( i ) = modulo ( a , 1 0 )

11 a = a / 1 0

12 a = floor ( a )

13 y ( i ) = modulo ( b , 1 0 )

14 b = b / 1 0

15 b = floor ( b )

16 end

17 d = x ( 1 ) + y ( 1 )

18 d b = d e c 2 b i n ( d )19 if d >9 then

20 d b = d e c 2 b i n ( d + 6 )

21 d b = d e c 2 b i n ( b i n 2 d e c ( d b ) - b i n 2 d e c ( ’ 1000 0 ’ ) )22 end

23 e = x ( 2 ) + y ( 2 )

24 e b = d e c 2 b i n ( e )

25 if d >9 then

26 e b = d e c 2 b i n ( e + 1 )

27 e = e + 1

28 end

29 if e >9

30 e b = d e c 2 b i n ( e + 6 )

31 e b = d e c 2 b i n ( b i n 2 d e c ( e b ) - b i n 2 d e c ( ’ 1000 0 ’ ) )32 end

44


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33 f = x ( 3 ) + y ( 3 )

34 f b = d e c 2 b i n ( f )35 if e >9 then

36 f b = d e c 2 b i n ( f + 1 )

37 f = f + 1

38 end

39 if f >9

40 f b = d e c 2 b i n ( f + 6 )

41 f b = d e c 2 b i n ( b i n 2 d e c ( f b ) - b i n 2 d e c ( ’ 1000 0 ’ ) )42 end

43 g = x ( 4 ) + y ( 4 )

44 g b = d e c 2 b i n ( g )

45 if f >9 then46 g b = d e c 2 b i n ( g + 1 )

47 g = g + 1

48 end

49 if g >9

50 g b = d e c 2 b i n ( g + 6 )

51 g b = d e c 2 b i n ( b i n 2 d e c ( g b ) - b i n 2 d e c ( ’ 1000 0 ’ ) )52 d c ( 5 ) = 1

53 end

54 d c ( 1 ) = b i n 2 d e c ( d b )

55 d c ( 2 ) = b i n 2 d e c ( e b )

56 d c ( 3 ) = b i n 2 d e c ( f b )

57 d c ( 4 ) = b i n 2 d e c ( g b )

58 z =0

59 for i =1 : 5

60 z = z + d c ( i ) * ( 1 0 ^ ( i - 1 ) )

61 end

62 disp ( z )

63 disp ( ’ e q u i v a l e n t b i n a r y fo rm ’ )64 p = strcat ( d e c 2 b i n ( d c ( 5 ) , 1 ) + d e c 2 b i n ( d c ( 4 ) , 4 ) + d e c 2 b i n (

d c ( 3 ) , 4 ) + d e c 2 b i n ( d c ( 2 ) , 4 ) + d e c 2 b i n ( d c ( 1 ) , 4 ) )

65 disp ( p )66 // a ns we r i s d i s p l a y e d //

45


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Scilab code Exa 3.3 Add 3 and 2 in XS3

1 // E xampl e 3−3//2 // add 3 and 2 i n E xc es s 3 c o de / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 n =3

8 m =2

9 z =0

10 a = 0 1 1 0

11 b = 0 1 0 1

12 e a = d e c 2 b i n ( n + 3 )

13 e b = d e c 2 b i n ( m + 3 )

14 for i =1: 4

15 x ( i ) = modulo ( a , 1 0 )

16 a = a / 1 0

17 a = floor ( a )

18 y ( i ) = modulo ( b , 1 0 )19 b = b / 1 0

20 b = floor ( b )

21 end

22 for i =1: 4

23 g ( i ) = b i t a n d ( x ( i ) , y ( i ) )

24 p ( i ) = b i t o r ( x ( i ) , y ( i ) )

25 end

26 c ( 1 ) = 0

27 for i =1: 4

28 c ( i + 1 ) = b i t o r ( g ( i ) , b i t a n d ( p ( i ) , c ( i ) ) )

29 end

30 if c ( 5 ) = = 1 then

31 z = d e c 2 b i n ( b i n 2 d e c ( e a ) + b i n 2 d e c ( e b ) + 3 )

32 end

46


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33 if c ( 5 ) = = 0 then

34 z = d e c 2 b i n ( b i n 2 d e c ( e a ) + b i n 2 d e c ( e b ) - 3 )35 end

36 disp ( ’ e q u i v a l e n t b i n ar y number a f t e r e x c e s s 3a d d i t i o n ’ )

37 disp ( z )

38 disp ( ’ e q u i v a l e n t d e c i m a l number ’ )39 disp ( m + n )


Scilab code Exa 3.4 Add 6 and 8 in XS3

1 // E xampl e 3−4//2 // add 6 and 8 i n E xc es s 3 c o de / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 n =6

8 m =8

9 a = 1 0 0 110 b = 1 0 1 1

11 e a = d e c 2 b i n ( n + 3 )

12 e b = d e c 2 b i n ( m + 3 )

13 for i =1: 4

14 x ( i ) = modulo ( a , 1 0 )

15 a = a / 1 0

16 a = floor ( a )

17 y ( i ) = modulo ( b , 1 0 )

18 b = b / 1 0

19 b = floor ( b )20 end

21 for i =1: 4

22 g ( i ) = b i t a n d ( x ( i ) , y ( i ) )

23 p ( i ) = b i t o r ( x ( i ) , y ( i ) )

47


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24 end

25 c ( 1 ) = 026 for i =1: 4

27 c ( i + 1 ) = b i t o r ( g ( i ) , b i t a n d ( p ( i ) , c ( i ) ) )

28 end

29 if c ( 5 ) = = 1 then

30 z = d e c 2 b i n ( b i n 2 d e c ( e a ) + b i n 2 d e c ( e b ) + 3 )

31 end

32 if c ( 5 ) = = 0 then

33 z = d e c 2 b i n ( b i n 2 d e c ( e a ) + b i n 2 d e c ( e b ) - 3 )

34 end

35 disp ( ’ e q u i v a l e n t b i n ar y number a f t e r e x c e s s 3

a d d i t i o n ’ )36 disp ( z )

37 disp ( ’ e q u i v a l e n t d e c i m a l number ’ )38 disp ( m + n )


Scilab code Exa 3.5 Convert binary 1011 to Gray code

1 // E xampl e 3−

5//2 / / b i n a r y t o g ra y c od e / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 a = 1 0 1 1

8 for i =1: 4

9 x ( i ) = modulo ( a , 1 0 )

10 a = a / 1 0

11 a = floor ( a )12 end

13 y ( 4 ) = x ( 4 )

14 k =3

15 while ( k > 0 )

48


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16 if b i t a n d ( x ( k + 1 ) , x ( k ) ) = = 1 then

17 y ( k ) = b i t c m p ( 1 , 1 )18 else

19 y ( k ) = b i t o r ( x ( k + 1 ) , x ( k ) )

20 end

21 k = k - 1

22 end

23 / / d i s p l a y / /24 z =0

25 for i =1: 4

26 z = z + y ( i ) * ( 1 0 ^ ( i - 1 ) )

27 end

28 disp ( ’ e q u i v a l e n t g ra y c od e ’ )29 disp ( z )

30 // e q u i v a l e n t g ra y c od e i s d i s p l a y e d //

Scilab code Exa 3.6 Convert binary 1001011 to Gray code

1 // E xampl e 3−6//2 / / b i n a r y t o g ra y c od e / /


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 a = 1 0 0 1 0 1 1

8 for i =1: 7

9 x ( i ) = modulo ( a , 1 0 )

10 a = a / 1 0

11 a = floor ( a )

12 end

13 y ( 7 ) = x ( 7 )14 k =6

15 while ( k > 0 )

16 if b i t a n d ( x ( k + 1 ) , x ( k ) ) = = 1 then

17 y ( k ) = b i t c m p ( 1 , 1 )

49


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18 else

19 y ( k ) = b i t o r ( x ( k + 1 ) , x ( k ) )20 end

21 k = k - 1

22 end

23 / / d i s p l a y / /24 z =0

25 for i =1: 7

26 z = z + y ( i ) * ( 1 0 ^ ( i - 1 ) )

27 end

28 disp ( ’ e q u i v a l e n t g ra y c od e ’ )29 disp ( z )

30 // e q u i v a l e n t g ra y c od e i s d i s p l a y e d //

Scilab code Exa 3.7 Convert Gray code 1011 to binary

1 // E xampl e 3−7//2 / / g ra y c od e t o b i n a ry / /3 clc


5 clear6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 a = 1 0 1 1

8 for i =1: 4

9 x ( i ) = modulo ( a , 1 0 )

10 a = a / 1 0

11 a = floor ( a )

12 end

13 y ( 4 ) = x ( 4 )

14 k =3

15 while ( k > 0 )16 if b i t a n d ( y ( k + 1 ) , x ( k ) ) = = 1 then

17 y ( k ) = b i t c m p ( 1 , 1 )

18 else

19 y ( k ) = b i t o r ( y ( k + 1 ) , x ( k ) )

50


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20 end

21 k = k - 122 end

23 z =0

24 for i =1: 4

25 z = z + y ( i ) * ( 1 0 ^ ( i - 1 ) )

26 end

27 disp ( ’ e q u i v a l e n t b i n a r y c od e ’ )28 disp ( z )

29 // e q u i v a l e n t b i na r y c od e i s d i s p l a y e d //

Scilab code Exa 3.8 Convert Gray code 1001011 to binary

1 // E xampl e 3−8//2 / / g ra y c od e t o b i n a ry / /3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 a = 1 0 0 1 0 1 1

8 for i =1: 79 x ( i ) = modulo ( a , 1 0 )

10 a = a / 1 0

11 a = floor ( a )

12 end

13 y ( 7 ) = x ( 7 )

14 k =6

15 while ( k > 0 )

16 if b i t a n d ( y ( k + 1 ) , x ( k ) ) = = 1 then

17 y ( k ) = b i t c m p ( 1 , 1 )

18 else19 y ( k ) = b i t o r ( y ( k + 1 ) , x ( k ) )

20 end

21 k = k - 1

22 end

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23 z =0

24 for i =1: 725 z = z + y ( i ) * ( 1 0 ^ ( i - 1 ) )

26 end

27 disp ( ’ e q u i v a l e n t b i n a r y c od e : ’ )28 disp ( z )

29 // e q u i v a l e n t b i na r y c od e i s d i s p l a y e d //

Scilab code Exa 3.9 Hamming code for 1011

1 // E xampl e 3−9//2 //Hamming cod e //3 clc

4 / / c l e a r s t h e command w in do w / /5 clear

6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 z = 1 0 1 1

8 // in pu t //9 a = 0 ; b = 0 ; c = 0 ; d = 0 ;

10 / / t a k i n g t h e i n p u t / /

11 for i = 1 : 712 x ( i ) = 0

13 if i = = 3 then

14 x ( i ) = 1

15 end

16 if i = = 5 then

17 x ( i ) = 1

18 end

19 if i = = 7 then

20 x ( i ) = 1

21 end22 end

23 // e s t a b l i s h i n g e v e n p a r i t y a t p o s i t i o n s 1 , 3 , 5 , 7/ /24 for i =1: 7

25 if x ( i ) = = 1 then

52


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26 a = a + 1

27 end28 end

29 d = modul o ( a , 2 )

30 if ( d = = 1 ) then

31 x ( 1 ) = 1

32 end


35 if ( i = = 5 ) then

36 continue

37 end

38 if ( x ( i ) = = 1 ) then39 b = b + 1

40 end

41 end

42 d = modul o ( b , 2 )

43 if ( d = = 1 ) then

44 x ( 2 ) = 1

45 end

46 // e s t a b l i s h i n g e v e n p a r i t y a t p o s i t i o n s 4 , 5 , 6 , 7/ /47 for i = 5 : 7

48 if ( x ( i ) = = 1 ) then

49 c = c + 1

50 end

51 end

52 d = modul o ( c , 2 )

53 if ( d = = 1 ) then

54 x ( 4 ) = 1

55 end

56 // d i s p l a y i n g t he r e s u l t //57 disp ( ’ t he hamming c od e f o r t h i s d at a i s g i ve n a s ’ )58 for i = 1 : 7

59 disp ( x ( i ) )60 end

53


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Scilab code Exa 3.10 Hamming code for 0101

1 // E xampl e 3−10//2 //Hamming cod e //3 clc

4 / / c l e a r s t h e command w in do w / /5 clear

6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 z = 0 1 0 1

8 // in pu t //9 a = 0 ; b = 0 ; c = 0 ; d = 0 ;

10 / / t a k i n g t h e i n p u t / /11 for i = 1 : 7

12 x ( i ) = 0

13 if i = = 3 then

14 x ( i ) = 1

15 end

16 if i = = 6 then

17 x ( i ) = 1

18 end19 end


22 if i = = 6 then

23 continue

24 end

25 if x ( i ) = = 1 then

26 a = a + 1

27 end

28 end

29 d = modul o ( a , 2 )

30 if ( d = = 1 ) then

31 x ( 1 ) = 1

32 end

54


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33 // e s t a b l i s h i n g e v e n p a r i t y a t p o s i t i o n s 2 , 3 , 6 , 7/ /

34 for i =2: 735 if x ( i ) = = 1 then

36 b = b + 1

37 end

38 end

39 d = modul o ( b , 2 )

40 if ( d = = 1 ) then

41 x ( 2 ) = 1

42 end

43 // e s t a b l i s h i n g e v e n p a r i t y a t p o s i t i o n s 4 , 5 , 6 , 7/ /44 for i = 5 : 7

45 if ( x ( i ) = = 1 ) then46 c = c + 1

47 end

48 end

49 d = modul o ( c , 2 )

50 if ( d = = 1 ) then

51 x ( 4 ) = 1

52 end

53 // d i s p l a y i n g t he r e s u l t //54 disp ( ’ t he hamming c od e f o r t h i s d at a i s g i ve n a s ’ )55 for i = 1 : 7

56 disp ( x ( i ) )

57 end

Scilab code Exa 3.11 Correction of Hamming code 1111101

1 // E xampl e 3−11//2 / / C o r r e c t i o n o f r e c e i v e d Hamming c o de / /


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 z = 1 1 1 1 1 0 1

55


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8 // i n c o r r e c t c od e t ak en a s i n pu t //

9 a = 0 ; b = 0 ; c = 0 ; d = 0 ;10 // t a k in g t he i n pu t i n an a r ra y //11 for i =1: 7

12 x ( i ) = 1

13 if i = = 2 then

14 x ( i ) = 0

15 end

16 end

17 / / c h e c ki n g f o r 4 , 5 , 6 , 7 e ve n p a r i t y //18 for i =4: 7

19 if x ( i ) = = 1 then

20 a = a + 121 end

22 end

23 d = modul o ( a , 2 )

24 if d = = 1 then

25 disp ( ’ w rong e n t r y f o r 4 , 5 , 6 , 7 ’ )26 x ( 4 ) = 1

27 else

28 disp ( ’ c o r r e c t e n tr y f o r 4 , 5 , 6 , 7 ’ )29 end

30 / / c h e c ki n g f o r 2 , 3 , 6 , 7 e ve n p a r i t y //31 for i =2: 7

32 if i = = 4 then

33 continue

34 end

35 if i = = 5 then

36 continue

37 end

38 if x ( i ) = = 1 then

39 a = a + 1

40 end

41 end42 d = modul o ( a , 2 )

43 if d = = 1 then

44 disp ( ’ w rong e n t r y f o r 2 , 3 , 6 , 7 ’ )45 x ( 2 ) = 1

56


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46 else

47 disp ( ’ c o r r e c t e n tr y f o r 2 , 3 , 6 , 7 ’ )48 end49 / / c h e c ki n g f o r 1 , 3 , 5 , 7 e ve n p a r i t y //50 for i =1: 7

51 if i = = 2 then

52 continue

53 end

54 if i = = 4 then

55 continue

56 end

57 if i = = 6 then

58 continue59 end

60 if x ( i ) = = 1 then

61 a = a + 1

62 end

63 end

64 d = modul o ( a , 2 )

65 if d = = 1 then

66 disp ( ’ c o r r e c t e n tr y f o r 1 , 3 , 5 , 7 ’ )67 x ( 1 ) = 1

68 else

69 disp ( ’ w rong e n t r y f o r 1 , 3 , 5 , 7 ’ )70 end

71 disp ( ’ T he re fo re , b i t 2 i s i n e r r o r and t he c o r r e c t e dc o d e i s : ’ )

72 for i =1: 7

73 disp ( x ( i ) )

74 end

75 // c o r r e c t c od e i s d i s p l a y e d //

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Chapter 4

Boolean Algebra

Scilab code Exa 4.1 Demorganize a function

1 // E xampl e 4−1//2 / / d e m o rg a n i ze f u n c t i o n / /3 clc



7 // t he g i ve n f u n c ti o n i s a s f o l l o w s //8 disp ( ’ G iv en f u n c t i o n − (AB ’ ’+C) ’ ’ ’ )9 disp ( ’ now d e m or g a ni z i ng t h e f u n c t i o n ’ )

10 disp ( ’ c om pl em en t f u n c t i o n ’ )11 disp ( ’ AB ’ ’+C ’ )12 disp ( ’ c h an g in g o p e r a t o r s ’ )13 disp ( ’ (A+B ’ ’ ) (C) ’ )14 disp ( ’ c om pl em en t v a r i a b l e s ’ )15 disp ( ’ ( A ’ ’ +B) ( C ’ ’ ) ’ )16 // f i n a l a ns w e r d i sp l ay e d a f t e r s i m p l i f i c a t i o n //

Scilab code Exa 4.2 Reduce an expression

58


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1 // E xampl e 4−2//

2 / / R ed u ci n g an e x p r e s s i o n / /3 clc4 // c l e a r s t he c o n s o l e //5 clear

6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 // t he g i ve n e x p r e s s i o n i s a s f o l l o w s //8 disp ( ’ G iv en E x p r e s si o n− A+B( C+(DE) ’ ’ ) ’ ’ ’ )9 disp ( ’ a p p l y i n g DeMo rga n t h e o r em ’ )

10 disp ( ’ r ed uc ed e x p r e s s i o n : ’ )11 disp ( ’ A+B(C+D ’ ’+E ’ ’ ) ’ ’ ’ )12 disp ( ’ A p p l y i n g DeMo rga n t h e o r em a g a i n ’ )

13 disp ( ’ A+B(C ’ ’DE) ’ )14 disp ( ’ T he re fo re f i n a l r e d u c e d e x p r e s s i o n i s : ’ )15 disp ( ’ A+BC ’ ’DE ’ )16 // f i n a l e x p r e s s i o n d i s pl a y e d //

Scilab code Exa 4.3 Reduce an expression

1 // E xampl e 4−3//

2 / / Re du ci ng a g i v e n e x p r e s s i o n //3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 // t he g i ve n e x p r e s s i o n i s a s f o l l o w s //8 disp ( ’ G iv en E x p r e s si o n− ( (AB) ’ ’+A ’ ’+AB) ’ ’ ’ )9 disp ( ’ ap pl y i ng DeM or gan T he or em ’ )

10 disp ( ’ r ed uc ed e x pr e s s i o n ’ )11 disp ( ’ (A ’ ’+B ’ ’+A ’ ’+AB) ’ ’ ’ )

12 disp ( ’ a s A+A=A ’ )13 disp ( ’ (A’ ’+B ’ ’+AB) ’ ’ ’ )14 / / By l a w 2 0 //15 disp ( ’ (A’ ’+B ’ ’+A) ’ ’ ’ )16 disp ( ’ r e a r r a n g i n g ’ )

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17 disp ( ’ (A+A ’ ’+B ’ ’ ) ’ ’ ’ )

18 / / by l aw 1 3/ /19 disp ( ’ (1+B ’ ’ ) ’ ’ ’ )20 / / by l aw 1 1/ /21 disp ( ’ 1 ’ ’ ’ )22 disp ( ’ 0 ’ )23 // f i n a l r ed uc ed e x p r e s s i o n i s d i s p la y e d /

Scilab code Exa 4.4 Reduce a boolean expression

1 // E xampl e 4−4//2 / / Re du ci ng a g i v e n e x p r e s s i o n //3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 // t he g i ve n e x p r e s s i o n i s a s f o l l o w s //8 disp ( ’ G iv en E x p r e s si o n− AB+(AC) ’ ’+AB ’ ’C(AB+C) ’ )9 disp ( ’ M u l t i p l y i n g ’ )

10 disp ( ’ AB+(AC) ’ ’+AABB ’ ’C+AB ’ ’CC ’ )

11 / / u s i n g l a w s 1 8 , 6 , 8 , 9 / /12 disp ( ’ AB+(AC) ’ ’+AB ’ ’C ’ )13 disp ( ’ a p p l y i n g DeMo rga n t h e o r em ’ )14 disp ( ’ AB+A ’ ’+C ’ ’+AB ’ ’C ’ )15 disp ( ’ r e a r r a n g e ’ )16 disp ( ’ AB+C ’ ’+A ’ ’+AB ’ ’C ’ )17 / / r e d uc e u s i n g l aw 2 0/ /18 disp ( ’ AB+C ’ ’+A ’ ’+B ’ ’C ’ )19 disp ( ’ r e a r r a n g i n g a g a i n ’ )20 disp ( ’ A ’ ’+AB+C ’ ’+B ’ ’C ’ )

21 / / r e d uc e u s i n g l aw 2 0/ /22 disp ( ’ A ’ ’+B+C ’ ’+B ’ ’ ’ )23 / / u s i n g l a ws 1 1 and 1 3/ /24 disp ( ’ 1 ’ )25 // f i n a l r ed uc ed e x p r e s s i o n i s d i s p la y e d //

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Scilab code Exa 4.5 Reduce a Boolean expression

1 // E xampl e 4−5//2 / / Red uce a g i v e n e x p r e s s i o n //3 clc



7 // t he g i ve n e x p r e s s i o n i s a s f o l l o w s //8 disp ( ’ G iv en E x p r e s si o n− ( (AB ’ ’+ABC) ’ ’+A( B+AB ’ ’ ) ) ’ ’

’ )9 disp ( ’ f a c t o r i s e ’ )

10 disp ( ’ ( (A(B ’ ’+BC) ) ’ ’+A(B+AB ’ ’ ) ) ’ ’ ’ )11 / / r e d uc e u s i n g l a ws 1 8 and 2 0/ /12 disp ( ’ ( (A(B ’ ’+C) ) ’ ’+A(B+A) ) ’ ’ ’ )13 disp ( ’ m u l t i p l y ’ )14 disp ( ’ ( (AB ’ ’+AC) ’ ’+AA+AB) ’ ’ ’ )15 / / r e d u c e u s i n g l a w s 7 , 8 , 1 1 , 1 8 / /16 disp ( ’ ( (AB ’ ’+AC) ’ ’+A) ’ ’ ’ )17 disp ( ’ de mo r gan i z e ’ )18 disp ( ’ ( (A ’ ’+B) (A ’ ’+C ’ ’ )+A) ’ ’ ’ )19 disp ( ’ m u l t i p l y ’ )20 disp ( ’ (A ’ ’A’ ’+A ’ ’C ’ ’+A ’ ’B+BC ’ ’+A) ’ ’ ’ )21 / / Red uc e u s i n g l a w s 1 8 , 8 / /22 disp ( ’ (A ’ ’(1+C’ ’+B)+BC ’ ’+A) ’ ’ ’ )23 / / r e d u c e u s i n g l aw 1 8 , 7 , 1 1 / /24 disp ( ’ 1 ’ ’ ’ )25 disp ( ’ 0 ’ )26 // f i n a l r ed uc ed e x p r e s s i o n i s d i s p la y e d //

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Chapter 6

Combinational Logic

Scilab code Exa 6.1 Convert A plus B to minterms

1 // E xampl e 6−1//2 / / c o n v e r t A+B t o m i n t er m s / /3 clc



7 / / c o n v e r s i o n t o m in te rm s / /8 disp ( ’ Given e x p r es s i o n − A+B ’ )9 disp ( ’ on s o l v i n g ’ )

10 disp ( ’ A(B+B ’ ’ )+B(A+A ’ ’ ) ’ )11 disp ( ’ m u l t i p l y i n g ’ )12 disp ( ’ AB+AB ’ ’+AB+A ’ ’B ’ )13 disp ( ’ we know A+A=A ’ )14 disp ( ’ AB+AB ’ ’+A ’ ’B ’ )15 // f i n a l r e s u l t i s d i sp l ay e d //

Scilab code Exa 6.2 Find minterms for A plus BC

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1 // E xampl e 6−2//

2 // f i n d mi nt e r ms f o r A+BC//3 clc4 // c l e a r s t he c o n s o l e //5 clear

6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 / / c o n v e r s i o n t o m in te rm s / /8 disp ( ’ G iv en e x p r e s s i o n − A+BC ’ )9 disp ( ’ on s o l v i n g ’ )

10 disp ( ’ A(B+B ’ ’ ) (C+C ’ ’ )+BC(A+A ’ ’ ) ’ )11 disp ( ’ (AB+AB ’ ’ ) (C+C ’ ’ )+BCA+BCA ’ ’ ’ )12 disp ( ’ m u l t i p l y i n g ’ )

13 disp ( ’ C ’ ’AB+AB ’ ’C+AB ’ ’C+AB ’ ’C ’ ’+BCA+BCA ’ ’ ’ )14 // f i n a l r e s u l t i s d i sp l ay e d //

Scilab code Exa 6.3 Find minterms for AB plus ACD

1 // E xampl e 6−3//2 // f i n d minterms f o r AB+ACD//3 clc


6 // c l e a r s a l l e x i s t i n g v a r i a b l e s //7 / / c o n v e r s i o n t o m in te rm s / /8 disp ( ’ Given e x p r es s i o n − AB+ACD ’ )9 disp ( ’ on s o l v i n g ’ )

10 disp ( ’ AB(C+C ’ ’ ) (D+D ’ ’ )+ACD(B+B ’ ’ ) ’ )11 disp ( ’ m u l t i p l y i n g ’ )12 disp ( ’ ABCD+ABC ’ ’D ’ ’+ABC’ ’D+ABCD ’ ’+AB ’ ’CD+ABCD ’ )13 disp ( ’ we know A+A=A ’ )

14 disp ( ’ ABC ’ ’D ’ ’+ABC ’ ’D+ABCD ’ ’+AB ’ ’CD+ABCD ’ )15

Digital Electronics- An Introduction to Theory and Practice_W. H. Gothmann

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Transcript of Digital Electronics- An Introduction to Theory and Practice_W. H. Gothmann