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GATE CSE 2021 Set 2 Q28: Binary fraction 0.1101 equals decimal 0.8xy5

Digital Logic
1 mark
NAT
No negative marking

If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$ , the decimal value of $x + y$ is ________.

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 3 (official GATE 2021 final answer key)

Concept used: Convert a binary fraction by summing negative powers of 2.

First step: $(0.1101)_2 = \tfrac12 + \tfrac14 + \tfrac1{16}$ ; write it as a decimal and read off $x$ and $y$ .

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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