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

Explain 100 line exchange with selector finder, Explain 100 line exchange w...

Explain 100 line exchange with selector finder. Design: In place of 100 two-motion selectors as in the case of Design 3, suppose we consider only 24 two-motion selectors. Whe

Sosail studies, whitch goods did the new england colonies exportto england ...

whitch goods did the new england colonies exportto england and what did they get in return

Signaling - universal serial bus , Signaling - Universal Serial Bus: U...

Signaling - Universal Serial Bus: USB supports following signaling rates: o   A low speed rate of 1.5 Mbit/s is defined by USB 1.0. This is so much similar to "full speed"

Combining logic gates - boolean algebra, More complicated logic circuits ca...

More complicated logic circuits can be made byconnecting a number of simple logic gates.How do we decide how to connect the gates togive a particular function e.g. output Y?We need

What is decision support system and describe its components, Q. What is a D...

Q. What is a DSS and Describe its components? A decision support system (DSS) is a highly flexible and interactive IT system that is designed to support decision making when t

Illustrate process of swapping system, What does the swapping system do if ...

What does the swapping system do if it identifies the illegal page for swapping? If the disk block descriptor does not have any record of the faulted page, then this causes the

Principles of contract law, Andrew, a 17 zear old university student decide...

Andrew, a 17 zear old university student decided to hold a post exams party for his friends. Andrew asked Kath, a family friend and the owner of 'Kath's Katerers' to supply food

Define overflow, Define Overflow.  An overflow is a problem in digital ...

Define Overflow.  An overflow is a problem in digital computer due to the width of registers is finite. A result that contains n+ 1 bit cannot be accommodated in a register wit

Technology enablers - information system, Technology Enablers - Information...

Technology Enablers - Information System The progression described above has been enabled by five main factors: Increases in processing capability allowing smaller and

Programming.., converting 10 ASCII characters to excess three using mplab i...

converting 10 ASCII characters to excess three using mplab ide

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