To understand base 2, or the binary system, you need to first understand base 10, or the decimal system, the system we use most often.

In the decimal system, each place value increases by a multiple of 10. The first 5 place values in the decimal system are:

10,000

1000

100

10

1

You may have seen base 10 blocks that look like this

So, in base 10, the number 32547 represents 3 ten-thousands, 2 thousands, 5 hundreds, 4 tens, and 7 ones.

If you would like more practice with base ten place values, try the following activities:

Video on place value with an interactive quiz

Place Value Party--a fun game where you trade candles on two birthday cakes.

However, there are other bases besides base 10. Base 2, or the binary system, uses only two numbers-0 and 1! Each place value increases by a multiple of 2. The first 5 numbers in the binary system are:

16

8

4

2

1

 

So, in base 2, the number 32547 represents 3 sixteens, 2 eights, 5 fours, 4 twos and 7 ones.

Here is a chart comparing base 10 numbers with their corresponding base 2 numbers.

Base 10	8`s	4`s	2`s	1`s	Base 2
1	0	0	0	1	0001
2	0	0	1	0	0010
3	0	0	1	1	0011
4	0	1	0	0	0100
5	0	1	0	1	0101
6	0	1	1	0	0110
7	0	1	1	1	0111
8	1	0	0	0	1000
9	1	0	0	1	1001
0	0	0	0	0	0000

 

To better understand binary system, try this fun activity:

My Binary Family Tree