Boolean Algebra & Logic Simplification.
SOP-Sum of Product - Product (SOP): Boolean equation written as sum of product terms
Cth:
POS-Product of Sum - sum (POS): Boolean equation written as product of sum terms
Cth:
Canonical Form of Boolean Algebra.
Cth:
A canonical SOP form consists of all minterms(m) that produce logic 1 Output
F(A,B,C) = ∑m(0, 3, 4, 5)
= m0+ m3 + m4+ m5
= A’B’C’ + A’BC + AB’C’ + AB’C
= 000 + 011+100+101
Cth:
A canonical POS form consists of all maxterms(M) that produce logic 0 output
F(A, B, C)
= ∏M(1, 2, 6, 7)
= M1• M2• M6• M7
= (A+B+C’)(A+B’+C)(A’+B’+C)(A’+B’+C’)
Cth:
Write the canonical SOP and canonical POS expression of the given truth table.
KARNAUGHMAP (K-MAP)
From K-map, an SOP expression can be obtained by grouping the logic 1 output.
Each output 1 on the K map must be included in at least one group. [In other words, all 1s must
grouped using minimum no. of groups.]
From K map, a POS expression can be obtained by grouping the logic 0 output.
Each output 0 on the K map must be included in at least one group. [In other words, all 0s must
grouped using minimum no. of groups.]