GATE CS 2021 Set 2 — Question 14
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Digital Logic → Number Systems & Arithmetic → IEEE 754 Floating Point
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Question
The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows:
Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
Correct answer
(C) exponent = 00000001 and mantissa = 00000000000000000000000
Solution
In the IEEE 754 single-precision standard:
1.Normalized numbers have an exponent field range from to (binary to ). The value is reserved for zero and subnormal numbers, and is reserved for infinity and NaN.
2.The smallest normalized positive number occurs when the exponent field is at its minimum value () and the mantissa (fraction) is at its minimum value ().
3.The implicit leading bit for normalized numbers is always .
Thus, the smallest normalized positive number has:- Exponent =
- Mantissa =
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