Determine the equivalent hexadecimal form of decimal number, Computer Engineering

Determine the equivalent hexadecimal form of decimal number, Computer Engineering

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Solve the equation 65.535₁₀ = X₁₆

Ans. In order to get X, convert the Decimal number 65.535 in its equal Hexadecimal form. So first taking 65 the integer part to convert in its equivalent Hexadecimal form.

2120_Determine the equivalent Hexadecimal form of Decimal number.png

Thus 65₁₀ = 41₁₆
After that take the decimal fractional part 0.6 for convert in its equivalent binary form.

Fraction	Fraction X 16	Remainder new fraction	Integer
0.535	8.56	0.56	8
0.56	8.96	0.96	8
0.96	15.36	0.36	15 (F)
0.36	5.76	0.76	5
0.76	12.16	0.16	12(C)
0.16	2.56	0.56	2
0.56	8.96	0.96	8

This is seen that this is impossible to find a zero as remainder even after 7 stages. So the process can be further continued or an approximation can be made as well as the process terminated now there. The Hexadecimal equivalent is 0.88F5C28.
Thus 65.535₁₀ = 41.88F5C28₁₆.

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