Digital-Logic-Design
November 23, 2023Digital-Logic-Design
November 23, 2023Digital-Logic-Design
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Question 5
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Consider the following representation of a number in IEEE 754 single-precision floating point format with a
bias of 127.
S : 1 E : 10000001 F : 11110000000000000000000
Here S, E and F 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 _______
bias of 127.
S : 1 E : 10000001 F : 11110000000000000000000
Here S, E and F 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 _______
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-7.75
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Question 5 Explanation:
Sign bit S= 1. The given number is a negative number.
Biased Exponent E = 27 + 1= 129
Actual Exponent e = E-127
= 129- 127
= 2
The decimal value= (-1)s x 1.M x 2e
= (-1) 1 x 1.1111 x 22
= – (111.11)
= – (7 + 0.75)
= -7.7
Correct Answer: A
Question 5 Explanation:
Sign bit S= 1. The given number is a negative number.
Biased Exponent E = 27 + 1= 129
Actual Exponent e = E-127
= 129- 127
= 2
The decimal value= (-1)s x 1.M x 2e
= (-1) 1 x 1.1111 x 22
= – (111.11)
= – (7 + 0.75)
= -7.7