Well explained.

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lets try to decode it...

since we have** 31 bits floating point number**... where **1 bit** reserved for **sign(s)** value.

and **bias value** = **127** . since **bias value**=* 2^{n-1} -1* =

so **bits reserved for exponent(e)** = **8bits**

**bits for mantissa(M)** = 31-(1+8) = **22bits.**

now... **normalized value** =** (-1) ^{s }* 1.M * 2**

since **BIASED EXPONENT= BIAS + AVAILABLE EXPONENT**

=>**AE** = (00111110)_{2}-127

= **-65**

so value = (-1)^{1} * 1.0000000001000000000000 * 2 ^{-65}

=-1 * (1+.0000000001000000000000) *2 ^{-65}

=** -1 * (1+ 2 ^{-10}) * 2 ^{-65}**

so answer is **option C**.

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