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Hexadecimal

Hexadecimal uses base 16 to count. Using our knowledge of bases and exponents we can construct a table to show the hexadecimal columns,

Column Number 8 7 6 5 4 3 2 1
Powers using base 16 167 166 165 164 163 162 161 160
Value 268435456 16777216 1048576 65536 4096 256 16 1


Of course if the second column is the number of 16s then we must devise some way of counting up to 16 using only 1 digit. To do this we use letters for the number 10 to 15.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 1 2 3 4 5 6 7 8 9 A B C D E F


We can then see that the hexadecimal number BC is calculated as

(B x 161) + (C x 160)

= (B x 16) + (C x 1)

= (11 x 16) + (12 x 1)

= 176 + 12

= 188

Next: Conversions