Question

Consider the following scenario and answer the question.

The single-precision 32-Bits (IEEE754) floating-point representation of the number 3.3 is 0 10000000 10100110011001100110011.  Is the single-precision floating-point representation of 3.3 precise? Please Explain your Answer.

Answer 1

--> Floating point representation is as follows:

             0              10000000            10100110011001100110011

           sign                exp                              mantissa

--> Sign bit tells it is positive

--> Exp value 10000000 = 128 in binary

--> After bias correction it is 128 - 127 = 1. So, exp is 2¹.

--> In mantissa the value stored is 1.649999976158142

--> So, after multiplying with exponent the actual value becomes,

                     3.2999999523162841796875

--> So, the single-precision floating-point representation of 3.3 is not precise. There is some error.