Question

Find the single-precision IEEE 754 representation of 0.752. Please show all work/steps.

Answer 1

The given number is:

= 0.752

The equivalent binary number is:

0.110000001000001100010010

The above number can be written as given below:

= 1.10000001000001100010010 x 2^-1   

The above notation is the standard normalized notation for the IEEE floating-point representation.

In single precision representation, 1 bit is used as a sign bit, 8 bits are used for the exponent, and 23 bits are used for the mantissa, and X-127 code is used.

The exponent will be:

-1 + 127 = 126

The binary representation of 126 in 8 bits is: 01111110

The IEEE single-precision representation is:

0 01111110 10000001000001100010010