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

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Official answer: 3

Number Representation and Arithmetic

Convert the fractional binary number $(0.1101)_2$ to its decimal equivalent:

(0.1101)_2 = 1 \times 2^{-1} + 1 \times 2^{-2} + 0 \times 2^{-3} + 1 \times 2^{-4}

(0.1101)_2 = 0.5 + 0.25 + 0 + 0.0625 = 0.8125

Equating this to $(0.8xy5)_{10}$ :

0.8125 = 0.8xy5

By comparing the digits:

$x = 1$
$y = 2$

Hence, the decimal value of $x + y$ is:

x + y = 1 + 2 = 3

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This Number Representation and Arithmetic previous year question is Q18 of the GATE CSE 2021 Set 2 paper. Find more GATE CSE PYQs on Number Representation and Arithmetic in Digital Logic, or browse all GATE CSE PYQs.

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Number Representation and Arithmetic in GATE CSE

Number Representation and Arithmetic has 33 GATE CSE PYQs across 20 papers from 2012 to 2026. 11 of them are 1-mark NAT questions like this one, and GATE CSE 2021 Set 2 has 2.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.