The IEEE floating point standard defines a single precision word to have $32$

bits. Of these, one bit is for the sign of the fraction, $8$ bits are used for the exponent, and

the remaining $23$ bits are for the fraction. A normalized representation is used for all the

numbers, except zero and the subnormal numbers. Assume that the extreme values at either

end of the exponent range are reserved for representing zero, Inf, NaN, subnormal numbers,

etc.