Floating-point Representation and Its Components

Computer Organization and Architecture2025-262 marksFloating point arithmetic operation

Explain floating-point representation and its components.

A floating point number stores a real number as a sign, an exponent and a fraction, in the form $(-1)^s \times 1.f \times 2^{e}$ .

Its components are:

Sign bit: 0 for positive and 1 for negative.
Exponent: the power of 2, stored with a bias so it is always positive. IEEE 754 single precision has 8 exponent bits and bias 127.
Fraction (mantissa): the digits after the implied leading 1. Single precision has 23 fraction bits.

The exponent sets the range and the fraction sets the accuracy.

A floating point number stores a real number as a sign, an exponent and a fraction, in the form $(-1)^s \times 1.f \times 2^{e}$.

Its components are:

Sign bit: 0 for positive and 1 for negative.
Exponent: the power of 2, stored with a bias so it is always positive. IEEE 754 single precision has 8 exponent bits and bias 127.
Fraction (mantissa): the digits after the implied leading 1. Single precision has 23 fraction bits.

The exponent sets the range and the fraction sets the accuracy.

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