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

Explain region, What is a Region? A Region is a continuous area of a p...

What is a Region? A Region is a continuous area of a process's address space (like text, data and stack). The kernel in a "Region Table" that is local to the process mainta

What is clipboard, Clipboard is a temporary storage location in Windows. Th...

Clipboard is a temporary storage location in Windows. The clipart will kept one piece of information at a time when it is manually added to the clipart or is copied there.

What are the various hazards encountered in pipelining, What is pipelining?...

What is pipelining? What are the various hazards encountered in pipelining? Explain in detail. The major characteristics of a pipeline are: a) Pipelining cannot be exe

Explain csmsginterface() function with predefined protocol, Explain CSMsgIn...

Explain CSMsgInterface() Function with Predefined Protocol A REQUEST structure is created for each message sent to the server. Messages passed to CSMsgInterface() as *dataMSG

Draw the logic diagram of 4-bit odd parity checkers, Normal 0 f...

Normal 0 false false false EN-IN X-NONE X-NONE

Find the de broglie wavelength of electron, Q. Find the de Broglie waveleng...

Q. Find the de Broglie wavelength of electron in the fourth orbit of hydrogen atom. We know that, λ = 2πr / n λ4 = 2πr 4 / 4 = 2π (4 2 r1) / 4 = 2 X

Back propagation learning routine, Back propagation Learning Routine - Aart...

Back propagation Learning Routine - Aartificial intelligence As with perceptrons, the information in the network is stored in the weights, so the learning problem comes down to

Draw layout cells in a table, Now add layout cells into which you will add ...

Now add layout cells into which you will add text about travel locations. 1. In Objects panel, click the Draw Layout Cell icon and move the pointer to layout table you just dre

Iterative deepening search, Iterative Deepening Search: So, breadth fi...

Iterative Deepening Search: So, breadth first search is always guaranteed to find a solution (if one exists), actually it eats all the memory. For the depth first search, ther

Command mode using vi editor, What does the c$ command do from command mode...

What does the c$ command do from command mode using Vi Editor? Ans) C$ will start from the character under the curser till the finish of line. So when you use this command it wi

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages