Bits and Bytes

At the smallest scale in the computer, information is stored as bits and bytes. In this section, we’ll look at how that works.

Bit

• Bit, like an atom, 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
•  -Nick’s tennis racket example
• Chip uses areas of electric charge as 0/1 states
• Hard drive uses spots North/South magnetism 0/1 states
• A bit is too small to be much use
• Group 8 bits into a byte

Everything in a computer is 0’s and 1’s … what does that mean? The bit stores just a 0 or 1 .. it’s the smallest building block of storage.

Byte

• One byte = grouping of 8 bits
• e.g. 0 1 0 1 1 0 1 0
• One byte can store one letter, e.g. ‘A’ or ‘x’

How much exactly can one byte hold?

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

• 3 bits vs. 2 bits
• Consider just the leftmost bit
• It can only be 0 or 1
• Lefmost bit is 0, then append 2-bit patterns
• Leftmost bit is 1, then append 2-bit patterns again
• Result … 3-bits has twice as many patterns as 2-bits

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

One Byte – 256 Patterns

• Need to know:
• 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 holds a number 0..255
• i.e. with 256 distinct patterns, we can store a number in the range 0..255
• Code: pixel.setRed(n) took a number 0..255. Why?
• The red/green/blue image numbers are each stored in one byte

Bytes

• “Byte” – unit of information storage
• A document, an image, a movie .. how many bytes?
• 1 byte is enough to hold 1 typed letter, e.g. ‘b’ or ‘X’
• Later we’ll look at storage in: RAM, hard drives, flash drives
• All measured in bytes, despite being very different hardware
• Kilobyte, KB, about 1 thousand bytes
• Megabyte, MB, about 1 million bytes
• Gigabyte, GB, about 1 billion bytes
• Terabyte, TB, about 1 trillion bytes (rare)

The space that data takes up in the computer is measured in by the “byte”. One byte is big enough to hold a single typed letter, like ‘a’. Here we’ll look at storing data in RAM memory and in persistent storage like a hard drive. All of that storage space will be measured in bytes. We’ll look at byte arithmetic in more detail later.

Bytes and Letters – ASCII Code

• ASCII is an encoding representing each typed letter by number
• Each number is stored in one byte of space in the computer (0..255)
• A is 65
• B is 66
• a is 96
• space is 32
• “Unicode” is an encoding for chinese, greek, arabic, etc. languages, typically 2-bytes per “letter”

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

• An example of bytes in your daily life
• When you type letters on your phone or computer
• Each letter is stored as a number in a byte, as below
• When you send, say, a text message, the numbers are sent
• Text is quite compact, using few bytes, compared to images etc.

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