To convert Fractional parts
From Compsci1
| Line 23: | Line 23: | ||
• This is the answer in binary code. | • This is the answer in binary code. | ||
| - | < | + | <pre> |
.375 | .375 | ||
x 2 | x 2 | ||
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1 .50 | 1 .50 | ||
x 2 | x 2 | ||
| - | 1 .00</ | + | 1 .00</pre> |
If we read the carried digits from the top down the answer is .0112 | If we read the carried digits from the top down the answer is .0112 | ||
Current revision as of 19:53, 11 October 2006
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
