Floating-Point IP Cores User Guide

ID 683750
Date 10/27/2021

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1.6.1. Floating-Point Formats

All floating-point formats have binary patterns. In the following figure, S represents a sign bit, E represents an exponent field, and M is the mantissa (part of a logarithm, or fraction) field.

For a normal floating-point number, a leading 1 is always implied, for example, binary 1.0011 or decimal 1.1875 is stored as 0011 in the mantissa field. This format saves the mantissa field from using an extra bit to represent the leading 1. However, the leading bit for a denormal number can be either 0 or 1. For zero, infinity, and NaN, the mantissa field does not have an implied leading 1 nor any explicit leading bit.

Figure 9. IEEE-754 Floating-Point FormatThis figure shows a floating-point format.