ISRO CS 2025 Q.49: solution and answer

ISRO 2025 · CSQ.49 · 1 mark · MCQ

If x and y are two decimal numbers such as $(0.11101)_{2} = (0.90 x y 5)_{10}$ , what are the values of x and y?

(A)
x = 2, y = 6
(B)
x = 6, y = 2
(C)
x = 9, y = 8
(D)
none of the above

See the question in the paper

Tap to open full size

Answer and solution

ANSWER

$x = 6, y = 2$ , which is option (b).

Official answer: BSource: ISRO's final answer key of 15 May 2026

A binary fraction $(0. b_{1} b_{2} b_{3} \dots)_{2}$ has value $\sum_{i} b_{i} 2^{- i}$ , so the bits after the point have weights $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}$ .
The bits of $(0.11101)_{2}$ are $1, 1, 1, 0, 1$ , so the value is $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + 0 + \frac{1}{32}$ .
In decimal: $0.5 + 0.25 + 0.125 + 0 + 0.03125 = 0.90625$ .
Compare $0.90625$ with $0.90 x y 5$ : after $0.90$ the digits are $6, 2, 5$ , so $x = 6$ and $y = 2$ .
This is option (b). Option (a) swaps the two digits and gives $0.90265$ , option (c) gives $0.90985$ , and since (b) fits, (d) is wrong.

KEY IDEA

Convert the binary fraction to decimal by adding the weights $2^{- i}$ of the 1 bits, then read off the required digits.

WATCH OUT FOR

Swapping the digits (choosing $x = 2, y = 6$ ), or forgetting that the fourth bit is 0 and the fifth bit contributes $\frac{1}{32} = 0.03125$ , not $\frac{1}{16}$ .

From the ISRO CS 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 2 ISRO Number systems questions, with notes