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

Datatype functions for message passing, Q. Datatype Functions for Message P...

Q. Datatype Functions for Message Passing? Datatype: It denotes type of data in message. This field is essential in the sense that MPI supports heterogeneous computing and diff

Power and energy, Ask questiPower and EnergyQuestion 4Consider a processor ...

Ask questiPower and EnergyQuestion 4Consider a processor that runs at 2.5 GHz and 1 Volt. When running a given CPU-bound program,the processor consumes 100 W, of which 20 W is leak

How putchar function is used within a c program, How putchar function is us...

How putchar function is used within a C Program ? The following program reads each character in the first line of input entered at the terminal's keyboard. It uses putchar to d

Real-time systems, This document is intended to help students get started w...

This document is intended to help students get started with the real-time systems (RTS) assignment. We will start on the assignment together in the laboratory. Students will then c

First-order models -artificial intelligence, First-Order Models - Artificia...

First-Order Models - Artificial intelligence: We proposed first-order logic like good knowledge representation language rather than propositional logic because it is more expre

What is the advantage of dividing an email address, What is the advantage o...

What is the advantage of dividing an email address into two parts? The division of an e-mail address in two parts is significant since it achieve two objectives. First, the div

Human intelligence in culture - artificial intelligence, Human intelligence...

Human intelligence in culture: Understand human intelligence in culture  "AI" can be seen as just the latest tool in the philosopher's toolbox for answering questions about

Is the data bus is bi-directional, The data bus is Bi-directional because t...

The data bus is Bi-directional because the similar bus is used for transfer of data among Micro Processor and memory or input / output devices in both the direction.

What are the types of pipeline hazards, What are the types of pipeline haza...

What are the types of pipeline hazards? The various pipeline hazards are:  1. Data hazard  2. Structural Hazard  3. Control Hazard.

Define the don''t care states - simplifying k maps, Define the Don't Care S...

Define the Don't Care States - Simplifying K Maps? The Truth table specifications for a logic function may not to include all possible combinations of the input binary digits for

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