Bits 'N' Bytes -- Words

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Words

Sixteen bits makes a word. So does four nibbles. Do does two bytes.

By combining the digits of 0 and 1, you can create 65,536 unique values ranging from 0000 0000 0000 0000 to 1111 1111 1111 1111. I'm putting spaces between the nibbles for easier reading,

Each bit in a word represents a power of 2 as you can see in this chart. Note that the "Bit Column" represents a digit position couting upwards from the right end of the byte towards the left.

Bit Column	Power of 2	Hex Value	Decimal Value
0	2⁰	1	1
1	2¹	2	2
2	2²	4	4
3	2³	8	8
4	2⁴	10	16
5	2⁵	20	32
6	2⁶	40	64
7	2⁷	80	128
8	2⁸	100	256
9	2⁹	200	512
10	2¹⁰	400	1,024
11	2¹¹	800	2,048
12	2¹²	1000	4,096
13	2¹³	2000	8,192
14	2¹⁴	4000	16,384
15	2¹⁵	8000	32,768

To represent, for example, a number 257 you would need a word of 0000 0001 0000 0001, with the right-most digit on the second nubble being a 256 and the right-most digit on the fourth nibble being 1, so 256 + 1 = 257. In hexadecimal, it's 01 01.

Once again, below is the bit value table. This applies to nibbles, which are bits in groups of four. Combine four of the nibbles to make a word.

Bits	Decimal Value	Hexadecimal Value
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
0111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F

Since bits are powers of 2, nibbles are basically powers of 16, and bytes are powers of 256.

The byte on the left represents 256¹, or 256, and the byte on the right represents 256⁰, or 1. Note that the "Byte Column" represents a digit position couting upwards from the right end of the word towards the left.

Byte Column	Power of 256	Hex Value	Decimal Value
0	256⁰	1	1
1	256¹	100	256

Here is an excerpt of the byte value table. Each byte is givin The actual table runs for 65,536 values.

Bytes in Decimal	Bytes in Hexadecimal	Decimal Value
0 0	00 00	0
0 16	00 10	16
0 64	00 40	64
0 255	00 FF	255
1 0	01 00	256
4 0	04 00	1024
16 0	10 00	4096
64 0	40 00	16,384
128 0	70 00	32,768
255 255	FF FF	65,535

32 bits form a Double Word or D-Word

Words

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