GATE CS 2021 Set 2 Q18 — Number Representations (Fixed and Floating Point)

x

and

y

are two decimal digits and

(0.1101)_2 = (0.8xy5)_{10}

, the decimal value of

x+y

is ___________

View worked solution

Answer: 3 : 3

To find the value of $x + y$ , we first convert the binary fraction $(0.1101)_2$ to its decimal equivalent:

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

Calculating each term:

1 \times 0.5 = 0.5

1 \times 0.25 = 0.25

0 \times 0.125 = 0

1 \times 0.0625 = 0.0625

Adding these values together:

0.5 + 0.25 + 0 + 0.0625 = 0.8125

Now, we compare this decimal representation with the given form $(0.8xy5)_{10}$ :

0.8125 = 0.8xy5

By matching the corresponding decimal places, we get:

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

x + y = 1 + 2 = 3

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Published 10 Oct 2026

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