Binary Numbers

First let me explain what you already know. In our normal base 10 system of counting, once a number passes 9, we go back to 0, and add one to the next column. So for example, the number 152 is really a 1 in the 100s column, a 5 in the 10s column and a 2 in the 1s column. So we are reading it as 100 + 50 + 2, or 152. Understand?

Well binary works in the same way, only instead of adding to the next column once you pass 9, you add to the next column once you pass one.

Back to base 10: A five digit number consists of a 10000s column, a 1000s column, a 100s column a 10s column and a 1s column.

Binary (or base 2): numbers are split up differently, and each digit doubles the one before it. There is a 1s column, a 2s column, a 4s column, an 8s column, a 16s column, a 32s column, a 64s column, etc. Although it might not come as naturally to humans, it is the same concept. You are basically adding together the numbers that each digit represents.

The number one is the same in both base 10 and binary: 1

The number two is different. In base 10 you just write "2", but in binary that digit does not exist. You put a 1 in the 2s column, and a 0 in the 1s column, so 2 is written as "10"

The number three is written as 3 in base 10 or as "11" in base 2. That means a 1 in the 1's column and a 1 in the 2's column. That adds up to make 3.

The number four is written as 4 in base 10, and as "100" in binary. That means 1 in the 4s column, and 0 in the 2s and 1s columns.

The number five is written as 5 in base 10, and as "101" in base 2. That is a 1 in the 4s column, a 0 in the 2s column, and a 1 in the 1s column. 4+0+1=5.

Get it? 10 isn't "ten", 10 is binary for 2. It's one of my favorite sayings :)

Here is a quick chart of some numbers:

1 = 1
2 = 10
3 = 11
4 = 100
5 = 101
6 = 110
7 = 111
8 = 1000
9 = 1001
10= 1010