Hexadecimal

Convert Hex to Binary, Decimal and back again

HEXADECIMAL

As seen in decimal and binary we use a Base 10 and Base 2 respectively. This means that in decimal (deci- means 10) we use 10 numbers, zero to 9 (0,1,2,3,4,5,6,7,8,9) = 10 numbers and then combinations of those numbers In binary, we use a Base 2 (or 2 numbers) these being 0 and 1

In hexadecimal, this is a Base 16 (or 16 numbers/symbols) This comprises of numbers 0-9 and A-F (ie 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F) In this case A=10, B=11, C=12, D=13, E=14 and F=15)

In Binary 15 is equivalent to 1111 (8+4+2+1) and 0 is equivalent to 0000

Lets say we wanted to convert 128 to Hexadecimal, we would need to covert it to Binary first, and then split it into 2 portions of 4 bits

Decimal	Binary	Hexadecimal
128	10000000	1000 | 0000 = 80

We split this up into 2 sets of 4 bits because Hexadecimal, the number 15 is F (1111), so in the case of 128, the Hexidecimal number is 8 and a 0 which equals 80.

So what about 255. Lets convert this to binary

Decimal	Binary	Hexidecimal
255	11111111	1111 | 1111 = FF
198	11000110	1100 | 0110 = C6
224	11100000	1110 | 0000 = E0

Lets try an IP Address, we will just work out the 10 and 1

IP	Binary	Hexidecimal
10.1.1.1	00001010.00000001	0000 | 1010 . 0000 | 0001 = 0A.01.01.01

My Table I Use:

Bits	128	64	32	16	8	4	2	1
Mask	128	192	224	240	248	252	254	255