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 about ip access, Explain about IP Access. IP access on the netw...

Explain about IP Access. IP access on the network by: • Intranets onto Virtual IP Networks and • Extranets onto Virtual IP Networks.

What is hyper-threading, Hyper-threading officially known as Hyper-threadin...

Hyper-threading officially known as Hyper-threading Technology (HTT) is Intel's trademark for their functioning of simultaneous multithreading technology on Pentium 4 micro-archite

What are the various design constraints, What are the various Design constr...

What are the various Design constraints used while performing Synthesis for a design? 1. Make the clocks (frequency, duty-cycle). 2. Explain the transition-time requirements

What are cosmic rays, Q. What are cosmic rays? The ionising radiation s...

Q. What are cosmic rays? The ionising radiation several times stronger than γ-rays entering the earth from all the directions from cosmic or interstellar space is known as cosm

Signaling pvm process, Q. Signaling PVM process? int pvm_sendsig( ...

Q. Signaling PVM process? int pvm_sendsig( int tid, int signum ) Transmits a signal to other PVM process. tid is task identifier of PVM process to receive signal.

Explain what is data mining, What is data mining? Data Mining: It...

What is data mining? Data Mining: It is an analytic process designed to explore data and after that to validate the findings through applying the detected patterns to lat

How are the instructions provided to computer, Let's answer our second ques...

Let's answer our second question first. All computers have a Unit which performs arithmetic and logical functions. This Unit is called as Arithmetic and Logic Unit (ALU). However h

Enumerate about the trackball device, Enumerate about the trackball A t...

Enumerate about the trackball A trackball is a two-dimensional positioning device, a spaceball provides six degrees of freedom. Unlike the trackball, a spaceball does not actua

Difference between blocking and non-blocking, Difference between blocking a...

Difference between blocking and non-blocking Verilog  language  has  two  forms  of  the  procedural  assignment  statement:  blocking  and  nonblocking. The two are distinguis

Determine the objectives of object oriented analysis, Objectives of object ...

Objectives of object oriented analysis After going through this unit, you should be able to: define the concepts of the objects in the system; express desired syste

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