Logarithmic Number System

A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing.

In LNS, a number, ${\displaystyle X}$, is represented by the logarithm, ${\displaystyle x}$, of its absolute value as follows:

where ${\displaystyle s}$ is a bit denoting the sign of ${\displaystyle X}$ (${\displaystyle s=0}$ if ${\displaystyle X>0}$ and ${\displaystyle s=1}$ if ${\displaystyle X<0}$).

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