GATE CS 2017 Set 2 — Question 12
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Digital Logic → Number Systems & Arithmetic → IEEE 754 Floating Point
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Question
Given the following binary number in 32-bit (single precision) IEEE-754 format:00111110011011011010000000000000The decimal value closest to this floating-point number is
Correct answer
(C) 2.27 × 10⁻¹
Solution
In IEEE-754 single precision (32-bit) format:
Value Comparing with options:
- Sign bit (): 1 bit
- Biased Exponent (): 8 bits
- Mantissa (): 23 bits
0 01111100 11011011010000000000000 1.Sign bit (): Positive number.
2.Biased Exponent (): .
Actual exponent .3.Mantissa (): The fractional part is
The significand is 4.Value:
Value Value Comparing with options:
- (A)
- (B)
- (C)
- (D)
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