• The binary equivalent of the fractional part is extracted from the products by reading the respective integral digits from the top downwards as shown by the arrow next page.
• Combine the two parts together to set the binary equivalent.

Convert 0.375₁₀ into binary form

Read this digits

0.375×2=0.750

0.750×2=1.500

0.500×2=1.000 (fraction becomes zero)

Therefore 0.375₁₀=0.011₂

NB: When converting a real number from binary to decimal, work out the integral part and the fractional parts separately then combine them.

Example

Convert 11.011₂ to a decimal number.

Solution

Convert the integral and the fractional parts separately then add them up.

2×1= 2.000

1×1= +1.000

3.000₁₀

Weight	21	20	.	2-1	2-2	2-3
Binary digit	1	1	.	0	1	1
Values in base 10	2	1	.	0	0.25	0.125

0.50×0 =0.000

0.25×1 =0.250

0.125×1=+0.125

0.375₁₀

3.000₁₀+0.375₁₀= 3.375₁₀

Thus 11.011₂=3.375₁₀

1. iv) Converting a decimal fraction to binary

Divide the integral part continuously by 2.For the fractional part, proceed as follows:

Multiply the fractional part by 2 and note down the product

• Take the fractional part of the immediate product and multiply it by 2 again.
• Continue this process until the fractional part of the subsequent product is 0 or starts to repeat itself.