To convert Fractional parts

From Compsci1

To convert fractional parts to binary

To convert numbers including fractional parts to binary or other bases we must deal with the whole part and the fractional part separately.

Eg:

Convert 43.375 to binary.

43 = 101 0112 – found by repeated division and noting remainders.

.375 • Multiply by 2

• Mark out digit carrying across the decimal point

• Continue multiplying the decimal only part by 2

• Mark each carry

• Repeat last 2 steps until you reach 0

• Read the carried digits from the top down

• This is the answer in binary code.

	.375
        x 2
0	.750
	x 2
1	.50
	x 2
1	.00

If we read the carried digits from the top down the answer is .0112

Exercise: Convert to binary

1. 0.5

2. 0.25

3. 0.125

4. 0.0625

5. 0.03125

6. 0.96875

7. 0.65625

8. 0.3125

9. 0.6875

10. 23.8125

11. 56.875

12. 37.8125