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DATA REPRESENTATION, BINARY SYSTEM, BIT, BYTE, ASCII CODEChapter 4
Lecturer In Charge: Manesh T
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DATA REPRESENTATION
• Data Representation refers to how Computers store lots of different types of information:
• numbers • text • graphics of many varieties (stills, video,
animation) • sound
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MEMORY STRUCTURE IN COMPUTER• Memory consists of bits (0 or 1)
– a single bit can represent two pieces of information
• bytes (=8 bits) – a single byte can represent 256 =
2x2x2x2x2x2x2x2 = 28 pieces of information • words (=2,4, or 8 bytes)
– a 2 byte word can represent 2562 pieces of information (approximately 65 thousand).
• Byte addressable - each byte has its own address.
3
BINARY SYSTEM
4
CLASSIFICATIONS
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STORAGE UNITS
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NUMBER SYSTEMS
Binary (2) Decimal (10) Octal (8)Hexadecimal
(16)0000' 0 0 0000'0001' 1 1 0001'0010' 2 2 0010'0011' 3 3 0011'0100' 4 4 0100'0101' 5 5 0101'0110' 6 6' 0110'0111' 7 7 0111'1000' 8 1000'1001' 9 1001'1010' 10 A1011' 11 B1100' 12 C1101' 13 D1110' 14 E1111' 15 F
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CONVERSION AMONG BASES
The possibilities:
Hexadecimal
Decimal Octal
Binary
pp. 40-468
QUICK EXAMPLE
2510 = 110012 = 318 = 1916
Base
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DECIMAL TO DECIMAL (JUST FOR FUN)
Hexadecimal
Decimal Octal
Binary
Next slide…10
12510 => 5 x 100 = 52 x 101 = 201 x 102 = 100
125
Base
Weight
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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 = 11 x 21 = 20 x 22 = 01 x 23 = 80 x 24 = 01 x 25 = 32
4310
Bit “0”
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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 = 42 x 81 = 167 x 82 = 448
46810
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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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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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EXAMPLE12510 = ?2
2 125 62 12 31 02 15 12 7 12 3 12 1 12 0 1
12510 = 11111012
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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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EXAMPLE7058 = ?2
7 0 5
111 000 101
7058 = 1110001012
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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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EXAMPLE10AF16 = ?2
1 0 A F
0001 0000 1010 1111
10AF16 = 00010000101011112
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CLASS WORK
Convert Decimal to Binary1. (421) 10 = ( ) 2
2. (1025)10 = ( ) 2
3. (368)10 = ( ) 2
4. (687)10 = ( ) 2
5. (625)10 = ( ) 2
6. (752)10 = ( ) 2
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CLASS WORK
Convert Binary to Hexadecimal1. (10110101001011100010)2 = ( )16
2. (10000100110110000101)2 = ( )16
3. (11100010101010011010)2 = ( )16
4. (10111100011011101101)2 = ( )16
5. (0101000110110101010)2 = ( )16
6. (101111111010011010)2 = ( )16
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CLASS WORK
Convert Hexadecimal to Binary1. (AF1) 16 = ( ) 2
2. (924)16 = ( ) 2
3. (3569)16 = ( ) 2
4. (4526)16 = ( ) 2
5. (6548)16 = ( ) 2
6. (1334)16 = ( ) 2
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ASCII
The most common code used in computers is ASCII (American Standard Code for Information Interchange).
ASCII provides codes for letters, digits, punctuation marks, and other special characters.
The ASCII code for A is 65 = 01000001
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ASCII CODESSp ! “ # $ % & ‘ ( ) * + , -
32 33 34 35 36 37 38 39 40 41 42 43 44 45
. / 0 1 2 3 4 5 6 7 8 9 : ;
46 47 48 49 50 51 52 53 54 55 56 57 58 59
< = > ? @ A B C D E F G H I
60 61 62 63 64 65 66 67 68 69 70 71 72 73
J K L M N O P Q R S T U V W
74 75 76 77 78 79 80 81 82 83 84 85 86 87
X Y Z [ \ ] ^ _ ` a b c d e
88 89 90 91 92 93 94 95 96 97 98 99 100 101
f g h i j k l m n o p q r s
102 103 104 105 106 107 108 109 110 111 112 113 114 115
t u v w x y z { | } ~
116 117 118 119 120 121 121 123 124 125 12634
ASCII REPRESENTATION OF TEXT
Since the ASCII codes for ART are
65, 82, and 84, the three bytes representing the word ART would be 01000001 0101010 01010100
• Nearly all software which deals with text (Notepad, WordPerfect, Word) use the ASCII codes to represent such text, though they may use proprietary codes to deal with fonts, etc.
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CHAPTER 4 END
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