Question 7.8: Determine the binary equivalent of decimal number 10.
Determine the binary equivalent of decimal number 10.
| Divide | 10 by 2 | 2|\underset{5}{\underline{10} } | 0 |
| Divide | 5 by 2 | 2|\underset{2}{\underline{5} } | 1 |
| Divide | 2 by 2 | 2|\underset{1}{\underline{2} } | 0 |
| Divide | 1 by 2 | 2|\underset{0}{\underline{1} } | 1 |
The remainders are impressed in reverse order to get the binary equivalent as 1010.
Conversion of fractional decimal number to fractional binary number
When the decimal number is a fraction, the conversion can be carried out through the following steps.
First, multiply the decimal fraction by 2. The result contains an integer part and a fractional part.
Separate the integer part and write it in a column. The fractional part becomes the new fraction. Repeat these steps till the fractional part becomes zero or the desired number of binary places are obtained. The 1s and 0s separated placed together gives the required fractional binary number. A few examples will illustrate the procedure.
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