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Consider the following bit pattern represents he floating point number in IEEE 754 single precision format :

1 10000111 11100000000000000000000

What is the value in Base-10 represented by above floating point number ?

1 10000111 11100000000000000000000

What is the value in Base-10 represented by above floating point number ?

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Best answer

Sign bit | Exponent (Biased) | Mantissa (Normalized) |

1 | 10000111 |
11100000000000000000000 |

Biased Exponent = $2^{n-1}-1$ = $2^{8-1}-1$ = 127

Number = $-1^{sign bit}$*1.M* $2^{Exponent-Biased Exponent}$

=> -1*1.11100000000000000000000*$2^{135-127}$

=>-1.11100000000000000000000*$2^8$

=>-111100000.000000000000000

=>(-480)$_{10}$

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