Binary Numbers

Introduction

A Binary Number is made up of only 0s and 1s.
Example: 110111

There is no 2, 3, 4, 5, 6, 7, 8 or 9 in Binary!

How do we Count using Binary?

It is just like counting in decimal except we reach 10 much sooner.

Binary Explanation
0 We start at 0
1 Then 1
??? But then there is no symbol for 2 … what do we do?

Well how do we count in Decimal?

Decimal Explanation
0 We start at 0
1 Then 1
2-8 Count 1,2,3,4,5,6,7,8
9 This is the last digit in Decimal
10 So we start back at 0 again, but add 1 on the left

The same thing is done in binary ...

Binary Explanation
0 We start at 0
1 Then 1
10 Now start back at 0 again, but add 1 on the left
11 1 more
??? But NOW what … ?

What happens in Decimal?

Decimal Explanation
99 When we run out of digits, we …
100 … start back at 0 again, but add 1 on the left

And that is what we do in binary ...

Binary Explanation
0 We start at 0
1 Then 1
10 Now start back at 0 again, but add 1 on the left
11 1 more
100 start back at 0 again, and add one to the number on the left but that number is already at 1 so it also goes back to 0 and 1 is added to the next position on the left
101  
110  
111  
1000 Start back at 0 again (for all 3 digits), add 1 on the left

See how it is done in this little demonstration

128
0
64
0
32
0
16
0
8
0
4
0
2
0
1
0
= 0