Exponent in Base 2
Computers work in the same way. The first column is the number of digits the computer has used. (Remember that a computer only has two.) This is the ones column. The second column is the number of times the computer has counted up using all of its two digits. This is the twos column. The third column is the number of times it has filled up the twos column. 2 x 2 is 4 so this is the fours column and so on.
- The number of 1s or 2^{0}
- The number of 2s or 2^{1}
- The number of 4s or 2^{2}
- The number of 8s or 2^{3}
And so on.
The first eight columns are
Column Number | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
Powers using base 2 | 2^{7} | 2^{6} | 2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} |
Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Adding up the binary number 11111111 we get (1 x 128) + (1 x 64) + (1 x 32) + (1 x 16) + (1 x 8) + (1 x 4) + (1 x 2) + (1 x 2) = 255. This is a very long number to only be able to count up to 255.
We are not very good at dealing with really long numbers and so to cut down on the number of digits we use a representation called hexadecimal.
Next: Hexadecimal