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Digital Basics Binary Numbers 1s_complement 2s_complement Binary Subtraction Binary Sub. Ex's Sign_magnitude SignM EX Gray Coding BCD coding Digital gates NAND NOR & XNOR Theorems Boolean Functions BFunc Examples Minterm Maxterm Sum of Minterms Prdt of Maxterms 2 var K-map 3 var K-map 4 var K-map 5 var K-map Prime Implicant PI example K-map Ex's KMap minimization 2 var EX

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Representation of Boolean functions in Canonical and Standard Forms:

Minterm or a standard product: Minterms are standard product terms obtained by AND operations on ‘n’ variables under discussion.

Suppose n = 2 (x and y)

and, we know ‘0’ represents complements i.e. x’ and y’

so, we have x, y, x’ and y’

Therefore, Minterms combinations are shown below.

Maxterm or standard sum: Maxterms are standard sum terms obtained by OR operation of ‘n’ variables and their complements.

Suppose n = 2 (x and y)

and, we know ‘0’ represents complements i.e. x’ and y’

so, we have x, y, x’ and y’

Generally, Maxterms are represented as complements of Minterms.

Therefore, Maxterm combinations are shown below.

x
y
Minterms
0
0
x’y’
0
1
x’y
1
0
xy’
1
1
xy
x
y
Minterms
Maxterms = (Minterms)’
0
0
x’y’
x + y
0
1
x’y
x + y’
1
0
xy’
x’ + y
1
1
xy
x’ + y’
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