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Consider the following format of 32 bit floating-point number:

(S) Sign: 1 bit
(E) Exponent: 8 bits
(M) Mantissa: 23 bits
The mantissa is normalized and has an implied "1" on the left of the point. Normalized form of mantissa is 1. M. The exponent is formatted using excess- 127 notation, with an implied base of 2. What will be the decimal value of the following 32 bit floating point number stored in the above-mentioned format?
  • a)
    -31.375
  • b)
    -7.843751
  • c)
    -15.6875
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider the following format of 32 bit floating-point number:(S) Sign...
Given,
The following format of 32 bit floating-point number:
(S) Sign: 1 bit
(E) Exponent: 8 bits
(M) Mantissa: 23 bits
As we know that,
Mantissa: 1.1111011= 1.960937510
Exponent: 10000011= 13110
Biased Exponent = 131 − 127 = 4
∵ Sign bit is 1.
It is a negative number.
= −1.9609375 × 24
= −31.375
Hence, the correct option is (A).
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Community Answer
Consider the following format of 32 bit floating-point number:(S) Sign...
Given,
The following format of 32 bit floating-point number:
(S) Sign: 1 bit
(E) Exponent: 8 bits
(M) Mantissa: 23 bits
As we know that,
Mantissa: 1.1111011= 1.960937510
Exponent: 10000011= 13110
Biased Exponent = 131 − 127 = 4
∵ Sign bit is 1.
It is a negative number.
= −1.9609375 × 24
= −31.375
Hence, the correct option is (A).
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Consider the following format of 32 bit floating-point number:(S) Sign: 1 bit(E) Exponent: 8 bits(M) Mantissa: 23 bitsThe mantissa is normalized and has an implied "1" on the left of the point. Normalized form of mantissa is 1. M. The exponent is formatted using excess- 127 notation, with an implied base of 2. What will be the decimal value of the following 32 bit floating point number stored in the above-mentioned format?a)-31.375b)-7.843751c)-15.6875d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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