The floating point no in its normalized form contain various attributes as follow:

1.Mantissa x 2 exponent

These floating point numbers can be represented using IEEE 754 format as given below.

1.Single precision format:

It is 32 bit format and uses the bias value of $127_{10}$ to calculate biased exponent.

2.Double precision format:

• It is 64 bit format and uses the bias value $(1023)_{10} \mu$ 3FFH to calculate biased exponent.

1. let us convert

$(178.625)_{10}$ into single precision format.

decimal no : $(178.625)_{10}$ Binary no : $(10110010.101)_2$

Normalized no :

Exponent - 7

Biased exponent : $(07 + 127) = (134)_{10}$

$= (1000 0110)_2$

Let us put mantissa and biased exponent in single precision IEEE 754 format.

1. Let us convert (178.625) 10 in double precision IEEE format :

Decimal no : $(178.625)_10$

Binary no :

Biased Exponent :

Let us put mantissa and BE in format :