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..
First, this is not the way standard IEEE P754 single precision floating point numbers are represented :


Exponent is not two's complement, there is instead an offset, for IEEE normalised : F=2^(Exponent - 127) * 1.Mantissa * Sign
Normalised numbers have an exponent different from 00 (being denormals) and FF (for infinites, NaN)


If this peculiar format has no implicit 1, mantissa should be between 0.10[..]0000 and 0.11[..]1111 :  Answer (D) or between 1.0000 and 1.11111, which is your proposal.

(IIRC, Intel double extended x87 80bits format does not have the implicit 1 and works as you describe. It is not striclty IEEE compliant, the 8087 being older than the standard.)