# Problem on Floating Point Representation

Consider the floating-point representation

31-24 : Exponent
23-0  : Mantissa


The exponent is in 2's complement representation and mantissa is in the sign magnitude representation. the range of the magnitude of the normalized numbers in this represntaion is

$(a)\ 0\ to \ 1$

$(b)\ 0.5\ to\ 1$

$(c)\ 2^{-23}\ to \ 0.5$

$(d)\ 0.5\ to \ (1-2^{-23})$

My approach: as the normalized number in floating point representation has as implicit 1.

Hence smallest mantissa would be

$1.0000\cdots [24\ 0's]=1$

Largest mantissa would be

$1.1111\cdots [24\ 1's]=1+(1-2^{-24})\approx2$

So my ans coming as 1 to 2, Which is not in the option. What mistake I'm doing..

• As given in the question numbers have to be normalized .Hence we are assuming an implicit 1. And one more thing all 0's in mantissa and exponent represents a 0 number and all 1's in mantissa and exponent represents an infinity. So I think smallest manitissa should be $1.0000...01=1+2^{-23}$ and largest possible mantissa should be $1.1111...10=1+(1-2^{-23})$. But still not in option. Jan 28, 2015 at 11:13