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Showing posts from April, 2010

Binary Digits.

Consider the number 783 which can be obtained by:
7 x102=7008 x101= 803 x100= 378310Total= 78310
In the decimal system, we are counting how many 10s, 100s, 1000s, 10000s etc. there are. Then we are multiplying the number depending on where it is positioned, and finally, we add them up.

If we were to do the same to the 8th base, then the above table will look as follows:

1 x83=5124 x82=2166 x81=487 x80=714678Total= 78310
Now the number 78310 ~= 14678. This means that any number (like 783) can be written to any number base; even its own. So in computers we are interested in binary digits, as the switches in circuits are either ON or OFF. With this in mind, the number above (783) would be written in binary form as follows:

1 x29=5121 x28=2560 x27=00 x26=00 x25=00 x24=01 x23=81 x22=41 x21=21 x20=111000011112Total= 78310

This means that:
11000011112 ~=78310

Here is a sequence that may simplify this process a bit better:

20 = 1 = 12
21 = 2 = 102
22 = 4 = 1002
23 = 8 = 10…