# Hexadecimal

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"Base 8 is just like Base 10 if you're missing 2 fingers. Shall we have a go at it?" *Tom Lehrer, New Math*

### Symbols

Binary only allows symbols for 0 and 1; anything bigger than 1 is represented with additional 0's and 1's in places with values of 2 raised to some power. 1010 = 1*2^{3} + 0*2^{2} + 1*2^{1} + 0*2^{0} = 8 + 0 + 2 + 0 = 10 (base 10). In base 2, there are 2 symbols (0 and 1). In base 10, there are ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). What if we wanted more symbols? We can grab them from the alphabet. The first new symbol would be A, the second B, and so on. This gives us enough symbols to work in Base 36 (if we can tell the difference between the number 0 and the letter O, between the number 1 and the letter l, and so on). In practice, the most popular number system for digital work is hexadecimal or base 16. It has the symbols 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F, representing decimal numbers from zero to 15.