Topic Content:
- Converting Denary Numbers to Binary Numbers
- Converting Binary Numbers to Base 10
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
= 1111two
b. 48
110000two
c. 29
= 11101two
d. 69
= 1000101two
Converting Binary Numbers to Base 10
Worked Example 1.5.2:
Convert the following binary numbers to denary numbers:
i. 10011two
ii. 100111two
Solution
i. 10011two = 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20
16 + 0 + 0 + 2 + 1 = 19ten
ii. 100111two =  1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 21 × 1 + 1 × 20
= 32 + 0 + 0 + 4 + 2+ 1 = 39ten
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