Explain single and double precision IEEE 754 binary floating point representation formats.

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written 5.7 years ago by

teamques10 ★ 69k

modified 5.7 years ago by

yashbeer ★ 11k

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:

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

2.Double precision format:

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

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

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

Normalized no : enter image description here

Exponent - 7

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

$= (1000 0110)_2$

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

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Decimal no : $(178.625)_10$

Binary no : enter image description here

Biased Exponent :

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Let us put mantissa and BE in format :

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