Tuesday, December 18, 2012

Logarithmic Number System

Introduction to Logarithmic Number System:

Logarithmic Number System ( LNS)  is a math type used to express the real numbers in computer and digital systems. LNS plays a major role in Digital image processing. The calculations in the digital systems are very difficult but this number system ( LNS) makes the math calculations very easy in the processor.In this article we are going to discuss logarithmic number system:

Logarithmic Number System

Logarithmic Number System Definition:

A number Z can be expressed in logarithmic definition as follows

`Z->{s,z = log_b(| Z |)}`

Where s is denoting the sign of Z

for example if `Z gt 0` then `s=0`

if `Z lt 0` then `s=1`

Where z is represented by binary number  that is  2's complement number.

For example the equivalent Binary number for 7 is 111

The Logarithmic number is considered as a Floating Point Number only  but asssume that the significant bit is always 1 In the processors the squaring and root finding for a number is difficult but the LNS reduces those calculations into simple addition and subtraction. Is this topic Distributive Property of Addition hard for you? Watch out for my coming posts.

Logarithmic Number System Calculations
logarithmic number system calculations

We know that the LNS can be used  make the calculations very easier in the processors. The calculations are,

Multiplication
Division


Multiplication:

The multiplication calculation is simple in the Logarithmic number system

For example

If we want to multiply the numbers M and N then in the logarithmic number system the calculation can be done as follows

`log_b(MxxN)= log_b(M) + log_b(N)`

Here the multiplication can be changed into addition so its more easier to calculate.

Division

The divsion calculation is simple in the Logarithmic number system

For example

If we want to divide the number M by the number N then in the logarithmic number system the calculation can be done by using the logarithmic property  as follows

`log_b(M/N)= log_b(M) - log_b(N)`

Here the division can be changed into Subtraction so it's more easier to calculate.

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