## Binary and Hexadecimal explanation and examples

For those of us who need a periodic review of binary and hexadecimal numbers, here is a quick look.

Decimal = Base 10
Binary = Base 2

(4 Bits)    (1 nibble)

0 0000 0 20 = 1
1 0001 1 21 = 2
2 0010 2 22 = 4
3 0011 3 23 = 8
4 0100 4 24 = 16
5 0110 6 25 = 32
6 0110 6 26 = 64
7 0111 7 27 = 128
8 1000 8 28 = 256
9 1001 9 29 = 512
10 1010 A 210 = 1024
11 1011 B 211 = 2048
12 1100 C 212 = 4096
13 1101 D 213 = 8192
14 1110 E 214 = 16384
15 1111 F 215 = 32768

4 bits per nibble, 1 nibble is 1 Hex digit
2 nibbles per byte (8 bits), 1 byte is 2 Hex digits
2 bytes per word (16 bits), 1 word is 4 Hex digits

4321 (Nibble #'s)
xxxx (Hex #)

(4)    (3)   (2)   (1)  (Nibble #'s)
xxxx   xxxx   xxxx   xxxx  (Bin #)
(15-12)(11-8) (7-4) (3-0) (Bit #'s)

Examples:

Bit 10 = 1:
0000 0100 0000 0000 (Bin)
0400 (Hex)

Bit 10=1, 11=1:
0000 1100 0000 0000 (Bin)
0C00 (Hex)

Bit 10=1, 11=1, 6=1, 1=1:
0000 1100 0100 0010 (Bin)
0C42 (Hex)

Bit 0=1, 1=1, 2=1, 3=1, 4=1, 5=1, 8=1:
0000 0001 0011 1111 (Bin)
013F (Hex)