GCSE Computing/Computing hardware/Introduction to Binary Logic/Binary logic/Bits Bytes Nibbles

What you need to know

Define the terms bit, nibble, byte

A bit

If we only have one wire (or other piece of data storage), it can be on or off. So we could only store a very small piece of information, such as if one thing were true (on) or false (off). This is called a bit.

A nibble

Usually we want to store more than true or false. It could be anything, but let's start simply with trying to store a moderate size number. If we had four bits together we could store 16 numbers (0 to 15).

Exercise

Check that you understand why four bits lets you store 16 different numbers, by writing out every possibility. The start and end of the table to do it is here:

Figure 1 - Table for a nibble

Eights	Fours	Twos	Ones	Equals
0	0	0	0	0
0	0	0	1	1
0	0	1	0	2
...	...	...	...	...
1	1	1	1	15

A byte

A nibble isn't a very useful amount. The main size up from a bit that people usually talk about is a byte, which is normally made up of 8 bits. If we had eight bits we could store 256 numbers (0 to 255).

Exercise

Check that you understand why eight bits lets you store 256 different numbers, by writing out the first ten numbers (0 to 9) and the last ten numbers (246 to 255).

ASCII Table

Let's look at trying to store a single letter. It's not as simple as 26 letters - we might need capitals or lower case, plus there are punctuation marks etc. The table below shows some of the characters available. If you look at the column headed Glyph it shows what letter or symbol it is. The Binary column tells you the binary equivalent. Again, think why we care about binary. A capital letter A, which has the binary 1000001 (65 in Base 10) means that, if this is being transmitted round a computer wires 1 and 7 have a voltage and the others don't.

Binary Oct Dec Hex Glyph 010 0000 040 32 20 ␠ 010 0001 041 33 21 ! 010 0010 042 34 22 " 010 0011 043 35 23 # 010 0100 044 36 24 $ 010 0101 045 37 25 % 010 0110 046 38 26 & 010 0111 047 39 27 ' 010 1000 050 40 28 ( 010 1001 051 41 29 ) 010 1010 052 42 2A * 010 1011 053 43 2B + 010 1100 054 44 2C , 010 1101 055 45 2D - 010 1110 056 46 2E . 010 1111 057 47 2F / 011 0000 060 48 30 0 011 0001 061 49 31 1 011 0010 062 50 32 2 011 0011 063 51 33 3 011 0100 064 52 34 4 011 0101 065 53 35 5 011 0110 066 54 36 6 011 0111 067 55 37 7 011 1000 070 56 38 8 011 1001 071 57 39 9 011 1010 072 58 3A : 011 1011 073 59 3B ; 011 1100 074 60 3C < 011 1101 075 61 3D = 011 1110 076 62 3E > 011 1111 077 63 3F ?

Binary Oct Dec Hex Glyph 100 0000 100 64 40 @ 100 0001 101 65 41 A 100 0010 102 66 42 B 100 0011 103 67 43 C 100 0100 104 68 44 D 100 0101 105 69 45 E 100 0110 106 70 46 F 100 0111 107 71 47 G 100 1000 110 72 48 H 100 1001 111 73 49 I 100 1010 112 74 4A J 100 1011 113 75 4B K 100 1100 114 76 4C L 100 1101 115 77 4D M 100 1110 116 78 4E N 100 1111 117 79 4F O 101 0000 120 80 50 P 101 0001 121 81 51 Q 101 0010 122 82 52 R 101 0011 123 83 53 S 101 0100 124 84 54 T 101 0101 125 85 55 U 101 0110 126 86 56 V 101 0111 127 87 57 W 101 1000 130 88 58 X 101 1001 131 89 59 Y 101 1010 132 90 5A Z 101 1011 133 91 5B [ 101 1100 134 92 5C \ 101 1101 135 93 5D ] 101 1110 136 94 5E ^ 101 1111 137 95 5F _

Binary Oct Dec Hex Glyph 110 0000 140 96 60 ` 110 0001 141 97 61 a 110 0010 142 98 62 b 110 0011 143 99 63 c 110 0100 144 100 64 d 110 0101 145 101 65 e 110 0110 146 102 66 f 110 0111 147 103 67 g 110 1000 150 104 68 h 110 1001 151 105 69 i 110 1010 152 106 6A j 110 1011 153 107 6B k 110 1100 154 108 6C l 110 1101 155 109 6D m 110 1110 156 110 6E n 110 1111 157 111 6F o 111 0000 160 112 70 p 111 0001 161 113 71 q 111 0010 162 114 72 r 111 0011 163 115 73 s 111 0100 164 116 74 t 111 0101 165 117 75 u 111 0110 166 118 76 v 111 0111 167 119 77 w 111 1000 170 120 78 x 111 1001 171 121 79 y 111 1010 172 122 7A z 111 1011 173 123 7B { 111 1100 174 124 7C | 111 1101 175 125 7D } 111 1110 176 126 7E ~

ASCII - more detail

You may wonder why the table above starts at 32 and not 0. The answer is that codes 0 to 31 are used for other things that aren't letters, such as a backspace or a new line character.