Define minterm and the maxterm - canonical form, Computer Engineering

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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.

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