Binary representation of information

Binary Representation of Numbers and Characters

In a computer, numbers are represented by numeric codes.

Representations of digits

Digits in base 10 (decimal):	`0 1 2 3 4 5 6 7 8 9`

Digits in base 16 (hex):	`0 1 2 3 4 5 6 7 8 9 A B C D E F`

Digits in base 8 (octal):	`0 1 2 3 4 5 6 7`

Digits in base 2 (binary):	`0 1`

Counting in different bases

What are the numbers after 9 in base 10?

10 11 12 ... 19 20 21 22 ... 99 100 101 ...

What are the numbers after F in base 16?

10 11 12... 19 1A 1B ... 1F 20 21 22 ... 99 9A 9B ... 9F A0 A1 ... A9 AA AB ... AF B0 ... FF 100 101 ...

What are the numbers after 7 in base 8?

10 11 12 ... 17 20 21 22 ... 77 100 101 ...

What are the numbers after 1 in base 2?

10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111

Using bases other than 10

In base 10:

16498 = 1*10⁴ + 6*10³ + 4*10² + 9*10¹ + 8*10⁰

In base 16:

16F98 = 1*16⁴ + 6*16³ + 15*16² + 9*16¹ + 8*16⁰
So, 16F98₁₆ = 94104₁₀

In base 8:

16475 = 1*8⁴ + 6*8³ + 4*8² + 7*8¹ + 5*8⁰
So, 16475₈ = 7485₁₀

In base 2:

11010 = 1*2⁴ + 1*2³ + 0*2² + 1*2¹ + 0*2⁰
So, 11010₂ = 26₁₀

What is the binary representation for 148?

Remember that:

2⁰ = 1 2¹ = 2 2² = 4 2³ = 8 2⁴ = 16 2⁵ = 32 2⁶ = 64 2⁷ = 128 2⁸ = 256 2⁹ = 512 2¹⁰ = 1024

ASCII Code

The most common code used in computers is ASCII (American Standard Code for Information Interchange). It provides encoding of letters, digits, punctuation marks, and other special characters.

Subset of ASCII code:


        sp  !  :  #  $  %  &  T  (  )  *  +  ,  -
        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
        88 89 90 91 92 93 94 95 96 97 98 99 100

         e   f   g   h   i   j   k   l   m   n
        101 102 103 104 105 106 107 108 109 110

         o   p   q   r   s   t   u   v   w   x
        111 112 113 114 115 116 117 118 119 120

         y   z   {   |   }   ~
        121 122 123 124 125 126