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GATE 2021 CS (CS2) – Question 28

Digital Logic · Number Representation and Arithmetic · 1 mark · Numerical answer

For decimal digits x,y, (0.1101)₂=(0.8xy5)₁₀. Find x+y.

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Correct answer: 3 to 3

Explanation

Convert the binary fraction: 1/2+1/4+0/8+1/16=0.8125. Comparing decimal digits gives x=1,y=2, so x+y=3. Leading fractional positions must retain their place values.

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