GATE CS 2026 Set 2 Q.34: Number Representations and Computer Arithmetic

The 32-bit IEEE 754 single precision representation of a number is 0xC2710000. The number in decimal representation is ________. (rounded off to two decimal places)

Your answer

Official answer and solution

Official answer: -60.25
From: Official GATE 2026 answer key

Solution

Decode the sign bit $S$ , 8-bit biased exponent $E$ , and 23-bit mantissa $M$ from 0xC2710000.

Converting 0xC2710000 to binary:

\text{C2710000}_{16} = \underbrace{1}_{S}\,\underbrace{10000100}_{E}\,\underbrace{11100010000000000000000}_{M}

Sign bit: $S = 1$ (negative).
Biased exponent: $E = 10000100_2 = 128 + 4 = 132$ , so true exponent $e = 132 - 127 = 5$ .
Significand: $1.M_2 = 1.1110001_2 = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{128} = 1 + \frac{113}{128} = \frac{241}{128}$ .

Value:

(-1)^1 \times \frac{241}{128} \times 2^5 = -\frac{241}{4} = -60.25

Final answer

-60.25

Common trap

Missing the negative sign when $S = 1$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 34 of 65
Section: Computer Science and Information Technology

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source