Define minterm and the maxterm - canonical form, Computer Engineering

Assignment Help:

Define Minterm and the Maxterm - Canonical Form?

Any Boolean expression perhaps expressed in terms of either minterms or maxterms. The literal is a single variable within a term which may or may not be complemented. For an expression with the N variables, minterms and maxterms are defined as follows:

A minterm is the product of the N distinct literals where each literal occurs exactly once.

A maxterm is the sum of the N distinct literals where each literal occurs exactly once.

For the two-variable expression, the maxterms and minterms are as follows

X

Y

Minterm

Maxterm

0

0

X'.Y'

X+Y

0

1

X'.Y

X+Y'

1

0

X.Y'

X'+Y

1

1

X.Y

X'+Y'

For a three-variable expression, the maxterms and minterms are as follows

X

Y

Z

Minterm

Designation

Maxterm

Designtion

0

0

0

X'.Y'.Z'

m0

X+Y+Z

M0

0

0

1

X'.Y'.Z

m1

X+Y+Z'

M1

0

1

0

X'.Y.Z'

m2

X+Y'+Z

M2

0

1

1

X'.Y.Z

m3

X+Y'+Z'

M3

1

0

0

X.Y'.Z'

m4

X'+Y+Z

M4

1

0

1

X.Y'.Z

m5

X'+Y+Z'

M5

1

1

0

X.Y.Z'

m6

X'+Y'+Z

M6

1

1

1

X.Y.Z

m7

X'+Y'+Z'

M7

 Consider a function F= x'y'z+xy'z'+xyz=m1+m4+m7

If we take the complement of F then F'= (x+y+z')(x'+y+z)(x'+y'+z')=M1.M4.M7

Any Boolean function can be expressed as a product of Maxterms and Sum of Minterms.


Related Discussions:- Define minterm and the maxterm - canonical form

Define memory cell, Define memory cell? A memory cell is capable of sto...

Define memory cell? A memory cell is capable of storing single bit of information. It is usually organized in the form of an array

Search in problem solving - artificial intelligence, Search in Problem Sol...

Search in Problem Solving: If Artificial Intelligence can inform that the other science about anything, it is about problem solving and, in particular, how to research after s

What are the various layers of a file system, What are the various layers o...

What are the various layers of a file system? The file system is composed of lots of dissimilar levels. Each level in the design uses the characteristic of the lower levels to

Explain management information base variables, Explain MIB (Management Info...

Explain MIB (Management Information Base) variables. MIB is a set of named items which an SNMP agent knows. To control or monitor a remote computer, a manager should fetch or s

Face scanning security system - biometric, Face Scanning Security System - ...

Face Scanning Security System - Biometric Computer Security Systems Finally, face scanning security system are also one of biometric technologies. Generally, the principle of

What is a deadlock, What is a Deadlock? Deadlock is a situation, in th...

What is a Deadlock? Deadlock is a situation, in that processes never complete executing and system resources are tied-up, preventing another job form starting. If the resou

What is index register, What is index register? In index mode the effec...

What is index register? In index mode the effective address of the operand is formed by adding a constant value to the contents of a register. The register used might be either

What is called when a star connected intermediate exchange, A star connecte...

A star connected intermediate exchange is known as a? A star connected intermediate exchange is termed as a Hub exchange.

Sigmoid units, Sigmoid units: Always remember that the function inside...

Sigmoid units: Always remember that the function inside units take as input the weighted sum, S and of the values coming from the units connected to it. However the function i

Transportation model, advantages and disadvantages of northwest corner meth...

advantages and disadvantages of northwest corner method and least cost method

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd