Denary
The numbers in normal use are called denary (or base 10)
The denary number system usea 10 digits that are 0 1 2 3 4 5 6 7 8 9
so 100 10 1
2 5 7 this number 257 would represent 2x100 + 5x10 + 7x1
Binary
The binary numbers system uses just two didits, 0 and 1
A binary digit is normally refered to as a bit and each bit is worth two times the digit to its immediate right
so 8 4 2 1
1 1 0 1 thus the binary number would represent 1x8 + 1x4 + 0x2 + 1x1 = 8 + 4 + 1 = 13
Denary to Binary
128 64 32 16 8 4 2 1
Place a 0 in the first column 0
87> 64 so place 1 in the column 0 1
Subtract 64 from 87 giving 23
23< 32 so place 0 in the column 0 1 0
23>16 so place 1 in the column 0 1 0 1
Subtract 16 from 23 giving 7
7<8 so place 0 in the column 0 1 0 1 0
7>4 so place 1 in the column 0 1 0 1 0 1
Subtract 4 from 7 giving 3
3>2 so place a 1 in the column 0 1 0 1 0 1 1
Subtract 2 from 3 giving 1
1 = 1 so place a 1 in the column 0 1 0 1 0 1 1 1
Subtract 1 from 1 giving 0
Hexadecima
The hexadecimal number system uses 16 digits that are 0 1 2 3 4 5 6 7 8 9 A B C D E F
Each digit is worth16 times a similar digit to its immediate right
so 256 16 1
1 C 5 As C represents twelve the hexidecimal number 1C5 would represent
1x256 + 12x16 + 5x1 = 256 + 192 + = 453
Binary to Hexidecimal
Divide the binary number into groups of four starting from the rightmost digit
In order to convert 0110111110010111
divide the number into groups of four giving 0110|1111|1001|0111
the hexidecimal number becomes 6 F 9 7
To translate from hexidecimal to binary reverse the process 1 A 5
0001 1010 0101
giving 000110100101 or (1100100101)