Karnaugh Map [K-Map]

• The key to minimizing a logic expression is the identification of logic adjacency
• Graphic representation of logic expression can facilitate identification of adjacency
• M. Karnaugh introduced (1953) a map to pictorially represent a logical expression.
• It is known as Karnaugh Map abbreviated as K-map.
• K-Map is a pictorial form of the truth-table.
• The inherent structure of the map facilitates systematic minimization
• K-map uses the ability of human perception to identify patterns and relationships when the information is presented graphically

Truth Table notation for Minterms and Maxterms 

Minterms and Maxterms are easy to denote using a truth table.

Example: Assume 3 variables x,y,z (order is fixed)

 

x	y	z	Minterm	Maxterm
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’yz’ = m2	x+y’+z = M2
0	1	1	x’yz = m3	x+y’+z’= M3
1	0	0	xy’z’ = m4	x’+y+z = M4
1	0	1	xy’z = m5	x’+y+z’ = M5
1	1	0	xyz’ = m6	x’+y’+z = M6
1	1	1	xyz = m7	x’+y’+z’ = M7