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

Listening sockets, a) What command do you use to list all listening sockets...

a) What command do you use to list all listening sockets? The output should also contain the name of the program to which the socket belongs. b) Write the command to use to

Authentication verses firewall, How does an authentication system be differ...

How does an authentication system be different from a firewall into functioning? Authentication verses firewall User Authentication and Authorization A significan

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

CPE, WHAT IS CPE

WHAT IS CPE

List the key notions concerning macro expansion, List the key notions conce...

List the key notions concerning macro expansion. Two key notions relating to macro expansion is: 1. Expansion time control flow- Determines the order of model statements tha

Define synchronous bus, Define synchronous bus. Synchronous buses are t...

Define synchronous bus. Synchronous buses are the ones in which every item is transferred during a time slot(clock cycle) known to both the source and destination units. Synchr

Input - output devices using device controller, Q. Input - output Devices u...

Q. Input - output Devices using Device Controller? A device controller needs not to necessarily control a single device. It can typically control multiple I/O devices. It come

Analysis of merge sort, i) The width of the sorting + merging circuit is eq...

i) The width of the sorting + merging circuit is equivalent to maximum number of devices needed in a phase is O(n/2). As in the above diagram maximum number of devices for a given

What is demand paging, What is major difference between the Historic Unix a...

What is major difference between the Historic Unix and the new BSD release of Unix System V in terms of Memory Management? Historic Unix uses Swapping - Whole process is tran

Use of intrinsic functions in fortran, Q. Use of Intrinsic Functions in FOR...

Q. Use of Intrinsic Functions in FORTRAN? HPF initiates some new intrinsic functions also to those defined in F90. The two mainly often used in parallel programming are system

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages