Teksti
- 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
- 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.