Lesson of the Week: Binary

We like round numbers. They are easy for us to understand because we were raised to round things to the nearest 10 based number. So for example, if you have $11 dollars in your pocket, you are apt to say you have about $10 on you. This is natural because our number system, the decimal system, is base 10. This means that there are 10 numbers in our system, 0 - 9. For example, 29 is made up of a 2 and a 9. 100 is made up of a 1 and two 0's.

This is not the only counting system. In fact you can have any based system you want. One system used a lot in the computing world is the binary system. Binary is a base 2 system, meaning there are only two numbers, 0 and 1. Obviously 0 = 0 and 1=1, but what about 2? Well, it works the same as the decimal system, you stick more numbers together to make bigger ones. So, 2 in decimal is 10 in binary. Three in decimal is 11 in binary. This pattern of switching 0's and 1's continues. A fast way to figure out the conversion is to remember each place as a value. So:

1   1   0   0   1 Binary
16  8   4   2   1 Decimal

The values of each place increase exponentially. So the rightmost column is worth 2^0. The next spot is worth 2^1, and so on. When there is a 0 in the column, there is no value from that column, when there is a 1 in the column, then add it into your final value. In this case we 11001 in binary is 16 + 8 + 0 + 0 + 1 = 25 in decimal. Not too bad huh? This can be a fun game to play with your kids! Well maybe not, but it is interesting.