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

Design a sample counter, Let's design a synchronous BCD counter. A BCD coun...

Let's design a synchronous BCD counter. A BCD counter follows a sequence of ten states and returns to 0 after count of 9. These counters are also known as decade counters. This typ

What are the engineering applications in parallel computing, Engineering Ap...

Engineering Applications A number of the engineering applications are: 1. Simulations of artificial ecosystems  2. Airflow circulation over aircraft components Airflow

Multiple instruction and multiple data stream (mimd), Multiple Instruction ...

Multiple Instruction and Multiple Data stream (MIMD): In this categorization, numerous processing elements and multiple control units are ordered as in MISD. However the differ

Write heterogeneous functions, Write "heterogeneous" functions If a pro...

Write "heterogeneous" functions If a program uses simulated, dynamically allocated multidimensional arrays, it becomes possible to write "heterogeneous" functions which don't h

.image forgery detection, what is the code to detect image forgery using Ma...

what is the code to detect image forgery using Matlab..??

How many types of memory in computer architecture, Computer have many type ...

Computer have many type of memory like primary memory , Auxiliary memory ,  Cache memory , buffer memory ,virtual memory , The work of all memory heterogeneously primary memory

Explain call by value and call by reference, Call by value and Call by refe...

Call by value and Call by reference Call by value means sending the values of the arguments- The value of each of the original arguments in the calling function is copied in

Combinatorial and scheduling problems, Combinatorial and Scheduling Proble...

Combinatorial and Scheduling Problems: One class of problems is concerned with specifying optimal scheduled. A classical example is the Travelling Salesperson Problem where

What is semaphores, What is semaphores?  A semaphore 'S' is a synchroni...

What is semaphores?  A semaphore 'S' is a synchronization tool which is an integer value that, apart from initialization, is accessed only by two standard atomic operations; wa

What is a parent class of all java classes, Parent class of all Java classe...

Parent class of all Java classes is? All Java class's parent class is java. lang.object.

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