ALGORITHMS AND PROGRAMMING - Kişisel Sayfalarkisi.deu.edu.tr/fidan.nuriyeva/CSC2201_03.pdf ·...
Transcript of ALGORITHMS AND PROGRAMMING - Kişisel Sayfalarkisi.deu.edu.tr/fidan.nuriyeva/CSC2201_03.pdf ·...
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ALGORITHMS AND PROGRAMMING
CSC 2201 Dokuz Eylul University, Faculty of Science,
Department of Mathematics
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Number Systems
System Base Symbols
Used by
humans?
Used in
computers?
Decimal 10 0, 1, … 9 Yes No
Binary 2 0, 1 No Yes
Octal 8 0, 1, … 7 No No
Hexa-
decimal
16 0, 1, … 9,
A, B, … F
No No
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Quantities/Counting
Decimal Binary Octal
Hexa-
decimal
0 0 0 0
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 5 5
6 110 6 6
7 111 7 7
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Quantities/Counting
Decimal Binary Octal
Hexa-
decimal
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
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Quantities/Counting
Decimal Binary Octal
Hexa-
decimal
16 10000 20 10
17 10001 21 11
18 10010 22 12
19 10011 23 13
20 10100 24 14
21 10101 25 15
22 10110 26 16
23 10111 27 17
Etc.
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Conversion Among Bases
The possibilities:
Hexadecimal
Decimal Octal
Binary
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Quick Example:
2510 = 110012 = 318 = 1916
Base
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Binary to Decimal
Hexadecimal
Decimal Octal
Binary
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Binary to Decimal
Technique
Multiply each bit by 2n, where n is the “weight” of the
bit
The weight is the position of the bit, starting from 0 on
the right
Add the results
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Example:
1010112 => 1 x 20 = 1
1 x 21 = 2
0 x 22 = 0
1 x 23 = 8
0 x 24 = 0
1 x 25 = 32
4310
Bit “0”
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Exercise:11
• 10112 = (?)10
Answer: 11
• 1010002 = (?)10
Answer: 40
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Octal to Decimal
Hexadecimal
Decimal Octal
Binary
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Octal to Decimal
Technique
Multiply each bit by 8n, where n is the “weight” of the
bit
The weight is the position of the bit, starting from 0 on
the right
Add the results
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Example:
7248 => 4 x 80 = 4
2 x 81 = 16
7 x 82 = 448
46810
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Exercise:15
• 368 = (?)10
Answer: 30
• 5648 = (?)10
Answer: 372
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Hexadecimal to Decimal
Hexadecimal
Decimal Octal
Binary
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Hexadecimal to Decimal
Technique
Multiply each bit by 16n, where n is the “weight” of
the bit
The weight is the position of the bit, starting from 0 on
the right
Add the results
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Example:
ABC16 => C x 160 = 12 x 1 = 12
B x 161 = 11 x 16 = 176
A x 162 = 10 x 256 = 2560
274810
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Exercise:19
• FA5416 = (?)10
Answer: 64084
• 5B1616 = (?)10
Answer: 23318
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Decimal to Binary
Hexadecimal
Decimal Octal
Binary
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Decimal to Binary
Technique
Divide by two, keep track of the remainder
First remainder is bit 0 (LSB, least-significant bit)
Second remainder is bit 1
Etc.
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Example:
12510 = ?2
12510 = 11111012
22
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Exercise:23
• 2710 = (?)2
Answer: 11011
• 17310 = (?)2
Answer: 10101101
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Octal to Binary
Hexadecimal
Decimal Octal
Binary
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Octal to Binary
Technique
Convert each octal digit to a 3-bit equivalent binary
representation
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Example:
7058 = ?2
7 0 5
111 000 101
7058 = 1110001012
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Exercise:27
• 2478 = (?)2
Answer:10100111
• 35678 = (?)2
Answer:011101110111
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Hexadecimal to Binary
Hexadecimal
Decimal Octal
Binary
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Hexadecimal to Binary
Technique
Convert each hexadecimal digit to a 4-bit equivalent
binary representation
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Example:
10AF16 = ?2
1 0 A F
0001 0000 1010 1111
10AF16 = 00010000101011112
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Exercise:31
• 1A616 = (?)2
Answer: 000110100110
• AE116 = (?)2
Answer: 101011100001
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