Binary System

The most widely used number base system after base 10 is the binary system because of its application to computers. In a binary system, the greatest digit used is 1, so the two digits available in the binary system are 0 and 1.

Binary system is called Base Two.

Converting Denary Numbers to Binary Numbers:

Worked Example 1.5.1:

Convert the following denary numbers to binary numbers:

a. 15
b. 48
c. 29
d. 69

Solution

a. 15

= 1111_two

b. 48

110000_two

c. 29

= 11101_two

d. 69

= 1000101_two

Converting Binary Numbers to Base 10

Worked Example 1.5.2:

Convert the following binary numbers to denary numbers:

i. 10011_two
ii. 100111_two

Solution

i. 10011_two = 1 × 2⁴ + 0 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰

16 + 0 + 0 + 2 + 1 =  19_ten

ii. 100111_two =   1 × 2⁵ + 0 × 2⁴ + 0 × 2³ + 1 × 2² + 2¹ × 1 + 1 × 2⁰

= 32 + 0 + 0 + 4 + 2+ 1  =  39_ten