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Bits and Bytes

At the smallest scale in the computer, information is stored as bits and bytes. In this section, we'll learn how bits and bytes encode information.

Bit

a "bit" is atomic: the smallest unit of storage

A bit stores just a 0 or 1

"In the computer it's all 0's and 1's" ... bits

Anything with two separate states can store 1 bit

In a chip: electric charge = 0/1

In a hard drive: spots of North/South magnetism = 0/1

A bit is too small to be much use

Group 8 bits together to make 1 byte

Everything in a computer is 0's and 1's. The bit stores just a 0 or 1: it's the smallest building block of storage.

Byte

One byte = collection of 8 bits

e.g. 0 1 0 1 1 0 1 0

One byte can store one character, e.g. 'A' or 'x' or '$'

How Many Patterns With N Bits? (demo)

How many different patterns can be made with 1, 2, or 3 bits?

Number of bits Different Patterns 1 0 1 2 00 01 10 11 3 000 001 010 011

100 101 110 111

3 bits vs. 2 bits

Consider just the leftmost bit

It can only be 0 or 1

Leftmost bit is 0, then append 2-bit patterns

Leftmost bit is 1, then append 2-bit patterns again

3-bits has twice as many patterns as 2-bits

Number of bits Different Patterns 1 0 1 2 00 01 10 11 3 0 00 0 01 0 10 0 11

1 00 1 01 1 10 1 11

In general: add 1 bit, double the number of patterns

1 bit - 2 patterns

2 bits - 4

3 bits - 8

4 bits - 16

5 bits - 32

6 bits - 64

7 bits - 128

8 bits - 256 - one byte

Mathematically: n bits yields 2n patterns (2 to the nth power)

One Byte - 256 Patterns (demo)

1 byte is group of 8 bits

8 bits can make 256 different patterns

How to use the 256 patterns?

How to store a number in a byte?

Start with 0, go up, one pattern per number, until run out of patterns

0, 1, 2, 3, 4, 5, ... 254, 255

One byte can hold a number between 0 and 255

i.e. with 256 different patterns, we can store a number in the range 0..255

Really good for storing characters/letters.

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Bytes

"Byte" - unit of information storage

A document, an image, a movie .. how many bytes?

1 byte is enough to hold about 1 typed character, e.g. 'b' or 'X' or '$'

All storage is measured in bytes, despite being very different hardware

Kilobyte , KB, about 1 thousand bytes

, KB, about 1 thousand bytes Megabyte , MB, about 1 million bytes , MB, about 1 million bytes Gigabyte , GB, about 1 billion bytes , GB, about 1 billion bytes Terabyte, TB, about 1 trillion bytes (rare)

Bytes and Characters - ASCII Code

ASCII is an encoding representing each typed character by a number

Each number is stored in one byte (so the number is in 0..255)

A is 65

B is 66

a is 96

space is 32

"Unicode" is an encoding for mandarin, greek, arabic, etc. languages, typically 2-bytes per "character" 32 space 33 ! 34 " 35 # 36 $ 37 % 38 & 39 ' 40 ( 41 ) 42 * 43 + 44 , 45 - 46 . 47 / 48 0 49 1 50 2 51 3 52 4 53 5 54 6 55 7 56 8 57 9 58 : 59 ; 60 < 61 = 62 > 63 ? 64 @ 65 A 66 B 67 C 68 D 69 E 70 F 71 G 72 H 73 I 74 J 75 K 76 L 77 M 78 N 79 O 80 P 81 Q 82 R 83 S 84 T 85 U 86 V 87 W 88 X 89 Y 90 Z 91 [ 92 93 ] 94 ^ 95 _ 96 ` 97 a 98 b 99 c 100 d 101 e 102 f 103 g 104 h 105 i 106 j 107 k 108 l 109 m 110 n 111 o 112 p 113 q 114 r 115 s 116 t 117 u 118 v 119 w 120 x 121 y 122 z 123 { 124 | 125 } 126 ~

Typing, Bytes, and You

Each letter is stored in a byte, as below

100 typed letters takes up 100 bytes

When you send, say, a text message, the numbers are sent

Text is quite compact, using few bytes, compared to images etc.

Numbers in Computers

web.stanford.edu - Bits and Bytes

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