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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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Product of Maxterms can be simply obtained by taking the complement of sum of Minterms from the Truth Table.

Example: Represent F = x + yz + xy in Product of Sum terms

F = (x + yz + x)(x + yz + y)

= (x + yz)(x + y +yz)

= (x + y)(x +z)(x + y + y)(x + y + z)

= (x +y)(x + z)(x + y)(x + y + z)

= (x +y + zz’)(x + z + yy’)(x +y +z)

= (x + y + z)(x +y + z’)(x + z + y)(x + z + y’)(x + y + z)

= (x + y + z)(x + y + z’)(x + y’ +z)

Answer.

Representation of Boolean Function in Product of Maxterms or Canonical Forms

x
y
z
Minterm in Function
Maxterm in Function
= (Minterm in Function)’
Maxterms
0
0
0
0
1
x + y+ z
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
x + y’ + z’
1
0
0
0
1
x’ + y + z
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0

F1 = (x + y + z)( x + y’ + z’ )( x’ + y + z)

Product of Sum terms function F1 is