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.
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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