Lesson 07 – The Binary Numbering System

The Binary Numbering System is a specific counting sequence for the various combinations of bits to follow from a low to a high count. This numbering system is similar to the normal decimal system we use everyday, but in place of having ten symbols per digit (0 to 9), there are only two, a 0 and a 1.

When we count in decimal we start at 0 and then 1, 2, 3, 4, up to 9, when we get to 9 we have reached the end of the available symbols. If count another count we carry a 1 over to represent a 10 and start at 0 again. The counting sequence is: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and the tenth count are 10.

When we count in binary we start at 0 and then 1 and then we have run out of symbols and we need to carry a 1 over to represent a 2 and start at 0 again. The counting sequence is: 0, 1 and then the second count are 10.

If we have a 8 bit binary number the bits will represent the following values where the least significant bit is on the right.

Binary

1

1

1

1

1

1

1

1

Bit no:

8

7

6

5

4

3

2

1

Value:

128

64

32

16

8

4

2

1

 Binary Bit Values

Decimal

Binary

 

Decimal

Binary

00

0000

08

1000

01

0001

09

1001

02

0010

10

1010

03

0011

11

1011

04

0100

12

1100

05

0101

13

1101

06

0110

14

1110

07

0111

15

1111

Decimal and Binary values