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 is post in terms of bios, For the one who still has no idea about the ...

For the one who still has no idea about the BIOS on your PC, notice when you first turn on your PC or laptop a few screens pop up. It may be a logo such as DELL or HP or ASUS, Tyan

Calculations for a standard vga graphics screen, Q. Calculations for a stan...

Q. Calculations for a standard VGA graphics screen? Let's do the calculations for a standard VGA graphics screen (640×480) using 16 colours. Total number of Pixels = 640 ×48

Split bus operation - universal serial bus , Split Bus Operation - universa...

Split Bus Operation - universal serial bus : USB 2.0 devices utilize a special protocol in the reset time that is called "chirping", to negotiate the high speed mode

Describe the importance of micro-programming, Question: (a) Describe t...

Question: (a) Describe the importance of Micro-Programming and point out one area where Micro-Programming is extensively used. (b) Below is a diagram of an 8086 processor.

Illustrate the uses of assembly language, Q. Illustrate the Uses of Assembl...

Q. Illustrate the Uses of Assembly Language? Uses of Assembly Language Assembly language is used mainly for writing short, efficient, specific interfacing modules/ subrou

How many address bits are needed to show a 32 K memory, How many address bi...

How many address bits are required to represent a 32 K memory ? Ans. 32K = 25 x 210 = 215, Hence 15 address bits are needed; Only 16 bits can address this.

Search mechanisms in prolog, Search mechanisms in Prolog: Here we can ...

Search mechanisms in Prolog: Here we can needs this simple Prolog program to describe how Prolog searches as:president(X) :- first_name(X, georgedubya), second_name(X, bush).

ECS, what is ecs?

what is ecs?

What do you mean by information system, Q. What do you mean by Information ...

Q. What do you mean by Information System? An information system is an planned combination of hardware, people, communication networks, software and data resources that transfo

What is the scope of public members in all classes, What is the Scope of pu...

What is the Scope of public/private/friend/protected/protected friend? Scope of public/private/friend/protected/protected friend. Visual Basic/Visual C# Public/pub

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages