Binary 101

Document Version 01

BINARY

Binary is the simplest method of counting for computers. Every single computer program is based on binary, without exception.

The concept is simple. You can have a yes or a no; true or false; left or right; up or down; black or white; right or wrong; but how do you convince a computer of that? Anybody who's tried to program anything in any language knows that 95% of the time, the computer is disagreeing with what you think you coded in the program.

So long ago, someone decided that in order for a computer to accept values of true or false, they would use numbers; 1 for true, 0 for false. The computer understood. That is the beginning of how binary changed your life.

So here's how binary works. We live in a decimal society, not binary, well, if you exclude technology. The word decimal comes from the Latin root Decimalis, meaning 10. The word Binary comes from the Latin meaning two.

In Practice

Let's start off simple.

1 is 1

Now in Binary, there are only ones and zeroes, so the next value is:

2 is 10

If you think about it, that's exactly what we do in decimal. For base-10, decimal, we go up to 9, 10 minus 1, then circle back to one again; same with binary. 2 - 1, then start over.

Here's the breakdown.

Decimal  -->  Binary

   1                       1
   2                      10
   3                      11
   4                     100
   5                     101
   6                     110
   7                     111
   8                    1000

Let's stop for a second. 2 to the third power equals 8. So, in Binary, every power of 2 is another restart, and the number of zeroes is determined by the power of 2.  So therefore..

16 --> 2x2x2x2 --> 10000 in Binary

...because there are 4 zeroes for each of the 2's necessary to multiply until you reach 16.