Boolean Algebra: Canonical Form
Boolean expressions can be expressed as canonical disjunctive normal form known as minterm, and as canonical conjunctive normal form known as maxterm. The sum of minterm is known as Sum Of Products or SOP, and the products of maxterm is known as Product Of Sum or POS.
The boolean functions expressed in the terms of products of minterms is or the products of maxterms is said to be in canonical form.
Example
Question:
Express the Boolean function F = xy + x’z as a product of maxterms
Solution:
F = xy + x’z
= (xy + x’)(xy + z)
= (x + x’)(y + x’)(x + z)(y + z)
= (x’ + y)(x + z)(y + z)
x’ + y = x’ + y + zz’
= (x’+ y + z)(x’ + y + z’) x + z
= x + z + yy’
= (x + y + z)(x + y’ + z) y + z
= y + z + xx’
= (x + y + z)(x’ + y + z)
F = (x + y + z)(x + y’ + z)(x’ + y + z)(x’ + y + z’)
= M0*M2*M4*M5
Therefore, POS is represented as Pi(0, 2, 4, 5)
Reference