Question

Can you help me to solve this problem

11101100111000110100010110011101 is a bit stream in IEEE754 format. Calculate the numerical value in decimal

Answer 1

To convert the floating point into decimal, we have 3 elements in a 32-bit floating point IEEE 754 representation.

Sign of Mantissa

This is as simple as the name. 0 represents a positive number while 1 represents a negative number.

Biased exponent

The exponent field needs to represent both positive and negative exponents. A bias is added to the actual exponent in order to get the stored exponent.

The Normalised Mantissa

The mantissa is part of a number in scientific notation or a floating-point number, consisting of its significant digits. Here we have only 2 digits, i.e. O and 1. So a normalized mantissa is one with only one 1 to the left of the decimal.

1 11011001 11000110100010110011101

The sign bit is 1, so a negative number, s=1

Exponent is decided by next 8 bits 11011001 => e = 217-127 = 90

Here, 127 is the unique number for 32-bit floating point representation. It is known as bias. It is determined by 2^k-1-1 where ‘k’ is the number of bits in exponent field.

The mantissa is calculated from the remaining 23 bits of the binary representation. It consists of ‘1’ and a fractional part which is determined by

The fractional part of mantissa is given by:
1*(2^-1) + 1*(2^-2) + 0*(2^-3) + 0*(2^-4) +………=0.7755

Thus the mantissa will be m=1+0.7755=1.7755

Hence, The decimal number given as

=