GATE CSE 2021 Set 2 Q14: Smallest normalized positive IEEE 754 single-precision number

The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows:

sign

exponent

mantissa

Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: C (official GATE 2021 final answer key)

Concept used: An all-zero exponent field is reserved for zero and denormals; normalized numbers start at exponent field 1.

First step: Take the smallest exponent field allowed for normalized numbers and the smallest mantissa: the value is $1.0 \times 2^{1-127}$ .

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key