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

State and prove demorgan’s first theorems, State and prove Demorgan’s First...

State and prove Demorgan’s First theorems: Ans. Statement of First Theorem of De Morgan: = A‾. B‾ Proof: The two sides of the equation i.e. = is represented with logic

What are the ways to create a new form, What are the ways to create a new f...

What are the ways to create a new form? You can make a new form in any of the following three ways: Using AutoForm: You can make a form based on a single table or query qui

What are the phases of video production, Question 1: a) What are the p...

Question 1: a) What are the phases of video production? b) What do you mean by storyboards? c) What are the differences between Point and Area (or Paragraph) Text?

What can be middle wares role within e-commerce, What can be middle wares r...

What can be middle wares role within e-commerce? By the utilize info Platform Commerce Server a shopping service can take benefit of reaching the end user onto Open TV, SMS, WA

What is data hazard in pipelining, What is data hazard in pipelining? What ...

What is data hazard in pipelining? What are the solutions? A data hazard is a situation in which the pipeline is stalled due to the data to be operated on are delayed for some

What is system software, What is system software? Give an example. It i...

What is system software? Give an example. It is a collection of program that are implemented as needed to perform functions such as I. Receiving and interpreting user comma

#title, what are the applications of microprogramming

what are the applications of microprogramming

own subprogram, Create your own Subprogram that uses at least 1input param...

Create your own Subprogram that uses at least 1input parameter and a return parameter. You decide the theme. You should give the pseudocode and an example Subroutine call. Be sure

QUELING SYSTEM, Q.SHOW THAT AVERAGE NUMBER OF UNIT IN A (M/M/1) QUELING SYT...

Q.SHOW THAT AVERAGE NUMBER OF UNIT IN A (M/M/1) QUELING SYTEM IS EQUAL TO P/(1-p). NOTE:P=ROW

Prototyping and incremental development, a) Write the main differences amo...

a) Write the main differences among prototyping and incremental development. b) Explain the commonality and main differences among agile approach and RUP.

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages