GATE CS 2021 Set 1 — Question 34
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Digital Logic → Number Systems & Arithmetic → IEEE 754 Floating Point
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Question
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.Here and denote the sign, exponent and fraction components of the floating point representation.The decimal value corresponding to the above representation (rounded to 2 decimal places) is ___________.
Correct answer
-7.75
Solution
To find the decimal value of the given IEEE 754 single-precision floating point representation:
The bias for single-precision is .
.
.
.The decimal value is .
1.Identify the components:
- Sign bit (): . Since , the number is negative.
- Biased Exponent (): . Converting this to decimal:
- Fraction (): . This represents the fractional part of the mantissa.
The bias for single-precision is .
.
3.Calculate the mantissa ():
In normalized form, the mantissa is ..
4.Calculate the final decimal value:
.The decimal value is .
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