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![Page 1: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/1.jpg)
Data Representation(in computer system)
![Page 2: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/2.jpg)
Data RepresentationData RepresentationHow do computers represent data?
1 1 1 1 1
0 0 0 0 0
The computers are digital
• Recognize only two discrete states: on or off
• Computers are electronic devices powered by electricity, which has only two states, on or off
on
off
![Page 3: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/3.jpg)
• The digital computer is binary.
• Everything is represented by one of two states:
• 0, 1 on, off true, false
• voltage, no voltage
• In a computer, values are represented by sequences of binary digits or bits.
How do computers represent data?
![Page 4: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/4.jpg)
Data Storage Units
• Bit : An abbreviation for BIbary digiT, is the smallest unit data representation.
• Byte (B)= 8bits
• KiloByte (KB) = 1024B
• MegaByte (MB) = 1024KB
• GigaByte (GB) = 1024MB
• TeraByte (TB) = 1024GB
![Page 5: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/5.jpg)
What is a byte?
Eight bits are grouped together to form a byte
0s and 1s in each byte are used to represent individual characters such as letters of the alphabet, numbers, and punctuation
![Page 6: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/6.jpg)
Data classification
Quantitative Qualitative
Not proportion to a value.
Name , symbols...
proportion to a value.Number
Integer Non Integer
![Page 7: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/7.jpg)
Data RepresentationData RepresentationWhat are two popular coding systems to represent data? American Standard
Code for Information Interchange (ASCII)
Extended Binary Coded Decimal Interchange Code (EBCDIC)
![Page 8: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/8.jpg)
How is a character sent from the keyboard to the computer?
Step 1:The user presses the letter T key on the keyboard
Step 2:An electronic signal for the letter T is sent to the system unit
Step 3:The signal for the letter T is converted to its ASCII binary code (01010100) and is stored in memory for processing
Step 4:After processing, the binary code for the letter T is converted to an image on the output device
![Page 9: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/9.jpg)
Number Systems
![Page 10: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/10.jpg)
Common Number Systems
System Base SymbolsUsed 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
160, 1, … 9,
A, B, … FNo No
![Page 11: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/11.jpg)
Quantities/Counting (1 of 2)
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
![Page 12: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/12.jpg)
Quantities/Counting (2 of 2)
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
![Page 13: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/13.jpg)
Quick Example
2510 = 110012 = 318 = 1916
Base
![Page 14: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/14.jpg)
2510 => 5 x 100 = 52 x 101 = 20
25
Base
Weight
![Page 15: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/15.jpg)
Number Base Conversion
• The possibilities:
Hexadecimal
Decimal Octal
Binary
![Page 16: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/16.jpg)
Binary to Decimal
Hexadecimal
Decimal Octal
Binary
![Page 17: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/17.jpg)
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
![Page 18: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/18.jpg)
Example
1010112 => 1 x 20 = 11 x 21 = 20 x 22 = 01 x 23 = 80 x 24 = 01 x 25 = 32
4310
Bit “0”
![Page 19: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/19.jpg)
Octal to Decimal
Hexadecimal
Decimal Octal
Binary
![Page 20: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/20.jpg)
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
![Page 21: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/21.jpg)
Example
7248 => 4 x 80 = 42 x 81 = 167 x 82 = 448
46810
![Page 22: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/22.jpg)
Hexadecimal to Decimal
Hexadecimal
Decimal Octal
Binary
![Page 23: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/23.jpg)
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
![Page 24: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/24.jpg)
Example
ABC16 => C x 160 = 12 x 1 = 12 B x 161 = 11 x 16 = 176 A x 162 = 10 x 256 = 2560
274810
![Page 25: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/25.jpg)
Decimal to Binary
Hexadecimal
Decimal Octal
Binary
![Page 26: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/26.jpg)
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.
![Page 27: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/27.jpg)
Example12510 = ?2
2 125 62 12 31 02 15 12 7 12 3 12 1 12 0 1
12510 = 11111012
![Page 28: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/28.jpg)
Octal to Binary
Hexadecimal
Decimal Octal
Binary
![Page 29: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/29.jpg)
Octal to Binary
• Technique– Convert each octal digit to a 3-bit equivalent
binary representation
![Page 30: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/30.jpg)
Example7058 = ?2
7 0 5
111 000 101
7058 = 1110001012
![Page 31: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/31.jpg)
Hexadecimal to Binary
Hexadecimal
Decimal Octal
Binary
![Page 32: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/32.jpg)
Hexadecimal to Binary
• Technique– Convert each hexadecimal digit to a 4-bit
equivalent binary representation
![Page 33: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/33.jpg)
Example10AF16 = ?2
1 0 A F
0001 0000 1010 1111
10AF16 = 00010000101011112
![Page 34: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/34.jpg)
Decimal to Octal
Hexadecimal
Decimal Octal
Binary
![Page 35: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/35.jpg)
Decimal to Octal
• Technique– Divide by 8– Keep track of the remainder
![Page 36: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/36.jpg)
Example123410 = ?8
8 1234 154 28 19 28 2 38 0 2
123410 = 23228
![Page 37: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/37.jpg)
Decimal to Hexadecimal
Hexadecimal
Decimal Octal
Binary
![Page 38: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/38.jpg)
Decimal to Hexadecimal
• Technique– Divide by 16– Keep track of the remainder
![Page 39: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/39.jpg)
Example123410 = ?16
123410 = 4D216
16 1234 77 216 4 13 = D16 0 4
![Page 40: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/40.jpg)
Binary to Octal
Hexadecimal
Decimal Octal
Binary
![Page 41: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/41.jpg)
Binary to Octal
• Technique– Group bits in threes, starting on right– Convert to octal digits
![Page 42: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/42.jpg)
Example10110101112 = ?8
1 011 010 111
1 3 2 7
10110101112 = 13278
![Page 43: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/43.jpg)
Binary to Hexadecimal
Hexadecimal
Decimal Octal
Binary
![Page 44: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/44.jpg)
Binary to Hexadecimal
• Technique– Group bits in fours, starting on right– Convert to hexadecimal digits
![Page 45: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/45.jpg)
Example10101110112 = ?16
10 1011 1011
2 B B
10101110112 = 2BB16
![Page 46: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/46.jpg)
Octal to Hexadecimal
Hexadecimal
Decimal Octal
Binary
![Page 47: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/47.jpg)
Octal to Hexadecimal
• Technique– Use binary as an intermediary
![Page 48: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/48.jpg)
Example10768 = ?16
1 0 7 6
001 000 111 110
2 3 E
10768 = 23E16
![Page 49: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/49.jpg)
Hexadecimal to Octal
Hexadecimal
Decimal Octal
Binary
![Page 50: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/50.jpg)
Hexadecimal to Octal
• Technique– Use binary as an intermediary
![Page 51: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/51.jpg)
Example1F0C16 = ?8
1 F 0 C
0001 1111 0000 1100
1 7 4 1 4
1F0C16 = 174148
![Page 52: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/52.jpg)
Exercise – Convert...
Don’t use a calculator!
Decimal Binary Octal
Hexa-decimal
33
1110101
703
1AF
Skip answer Answer
![Page 53: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/53.jpg)
Exercise – Convert…
Decimal
Binary Octal
Hexa-decimal
33 100001 41 21
117 1110101 165 75
451 111000011 703 1C3
431 110101111 657 1AF
Answer
![Page 54: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/54.jpg)
Binary Addition
• Two n-bit values– Add individual bits– Propagate carries– E.g.,
10101 21+ 11001 + 25 101110 46
11
![Page 55: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/55.jpg)
Multiplication
• Binary, two n-bit values– As with decimal values– E.g., 1110
x 1011 1110 1110 0000 111010011010
![Page 56: Data Representation (in computer system). Data Representation How do computers represent data? 1111111111 0000000000 b The computers are digital Recognize.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bf821a28abf838c859e7/html5/thumbnails/56.jpg)
Thank you