Determine the equivalent binary form of decimal number, Computer Engineering

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Solve the equation 23.610 = X2 for X

Ans. 23.610 = X2

So as to find X, firstly convert the Decimal number 23.610 in its Binary form. After that take the decimal integer part 23 to convert in its equivalent binary form,

2368_Determine the equivalent binary form of Decimal number.png

Thus2310 = 101112
After that take the decimal fractional part 0.6 to convert in its equivalent binary form.

Fraction

Fraction X 2

Remainder new

fraction

Integer

0.6

1.2

0.2

1

0.2

0.4

0.4

0

0.4

0.8

0.8

0

0.8

1.6

0.6

1

0.6

1.2

0.2

1

0.2

0.4

0.4

0

0.4

0.8

0.8

0

This is seen that this is impossible to finda zero as remainder still after 7 stages. This process can be further continued or an approximation can be made as well as the process terminated now. The binary equivalent is 0.1001100.
Thus23.610 = 10111.10011002.


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