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# 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 |