Determine the equivalent binary form of decimal number, Computer Engineering

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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