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

What do you call an event and when do you call an assertion, What do you ca...

What do you call an event and when do you call an assertion? Assertion based Verification Tools, checks whether a statement holds a explained  property or not, while, Event bas

Explain e-brokerage, E-brokerage. An e-brokerage is an investment house...

E-brokerage. An e-brokerage is an investment house that permits you to buy and sell stocks and get investment information from its Web site.

What is tri-state logic, Three Logic Levels are used and they are High, Low...

Three Logic Levels are used and they are High, Low, High impedance state. The high and low are normal logic levels & high impedance state is electrical open circuit conditions. Tri

What is canonical and standard forms, Q.What is Canonical and Standard Form...

Q.What is Canonical and Standard Forms? An algebraic expression can express in two forms: i) Sum of Products   (SOP) for example (A . B¯) + (A¯ . B¯)            ii) Produ

How to insert script in dreamweaver, Q. How to insert script in dreamweaver...

Q. How to insert script in dreamweaver? Step 1: Click on Insert Step 2: Click on Script Step 3: Choose the type of Script Step 4: Write the code in "Content" Step 5: T

Diffrentiate between non-relocatable & relocatable programs, How non-reloca...

How non-relocatable programs are different from relocatable programs? Non relocatable program: It is one that cannot be made to execute in any type of area of storage other t

What are the elements of an instruction, Q. What are the elements of an ins...

Q. What are the elements of an instruction? As the function of instruction is to communicate to CPU what to do it needs a minimum set of communication such as:  What op

Explain basic time division and time switching method, What is time divisio...

What is time division switching? With the help of block diagram explain basic time division and time switching method. Time Division Switching: A switching component can be s

Show the decimal equivalent of a binary number, Q. Show the Decimal equival...

Q. Show the Decimal equivalent of a binary number? In binary numbers we have two digits 0 and 1 in addition they can also be signified as a string of these two-digits known as

What do you understand by electronic funds transfer, What do you understand...

What do you understand by Electronic Funds Transfer?  Electronic Funds Transfer: It's an electronic payment method that transfers the money value from one bank account to

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