Floating-point representation
Coding numbers in computers

For all representations, the number of different numbers is exactly the same: 2ⁿ for n bits. The characteristic of integer and fixed-point representations is that the gap between two successive numbers is always the same: 1 for integers, 2^–k for fixed-point with k bits after the decimal point. The range of numbers that can be represented is limited: from 0 to 2ⁿ – 1 for unsigned integers and from –2^n–1 to 2^n–1 – 1 for signed integers. For fixed-point representation, the above amplitudes are divided by 2^k when there are k bits after the decimal point.

The aim of floating-point representation is to increase the amplitude of numbers that can be represented with variable gaps between two successive numbers.