Question 66

Computer Awareness Number representations Easy

Given the following binary number in 32-bit (single precision) IEEE-754 format:00111110011011010000000000000000.

The decimal value closest to this floating-point number is

(A) \( 1.45 \times 10^{1} \)
(B) \( 1.45 \times 10^{-1} \)
(C) \( 2.27 \times 10^{-1} \)
(D) \( 2.27 \times 10^{1} \)
✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Split the 32 bits: 0 | 01111100 | 11011010000…

  • Sign = 0, so the number is positive.
  • Exponent = \(01111100_2 = 124\). Actual exponent = \(124 - 127 = -3\).
  • Mantissa = \(1.1101101_2 = 1 + 0.5 + 0.25 + 0.0625 + 0.03125 + 0.0078125 = 1.8515625\).

Value = \(1.8515625 \times 2^{-3} \approx 0.2314\).

The closest option is \(2.27 \times 10^{-1}\).

Answer: (C)

Practice Similar Number representations Questions

Reinforce your conceptual grasp with related questions from CUET-MCA 2023:

Q52 A 2's-complement adder-subtracter can add or subtract binary numbers....
Solve →
Q75 The number of 1 's in the binary representation of (3* 4096+15 *...
Solve →
Q28 The amount of time required to read a block of data from a disk into...
Solve →
Q30 A 32 bit wide main memory with a capacity of 1 GB is built using \( 256 ~M...
Solve →
Q33 If \( \) and \( \) denote the exclusive OR and exclusive NOR operations,...
Solve →
Full-Length Test Series

Prepare for CUET-MCA Under Real Exam Conditions

Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.

Start Free Mock Test Series →