ECE18R277 DIGITAL ELECTRONICS Dr. GANESHAPERUMAL DHARMARAJ DEPARTMENT OF INSTRUMENTATION AND CONTROL ENGINEERING KALASALINGAM ACADEMY OF RESEARCH AND EDUCATION August 25, 2020 Dr. GANESHAPERUMAL DHARMARAJ ECE18R277 1/7 Karnaugh-Map(K-Map) Minterm: A minterm of n variables = product of n literals in which each variable appears exactly once either in T or F form, but not in both. (Also known as a standard product term) Each minterm has value 1 for exactly one combination of values of variables. E.g. ABC (111) = m7 A function can be written as a sum of minterms, which is referred to as a minterm expansion or a standard sum of products. Dr. GANESHAPERUMAL DHARMARAJ ECE18R277 2/7 Karnaugh-Map(K-Map) Minterm Notation: f = A’BC + AB’C’ + AB’C + ABC’ +ABC; The other way to represent f is: 1 2 f (A,B,C) = m P3 + m4 +m5 +m6 +m7 f (A,B,C) = m (3,4,5,6,7) Minterms present in f correspond with the 1’s of f in the truth table. Dr. GANESHAPERUMAL DHARMARAJ ECE18R277 3/7 Karnaugh-Map(K-Map Minterm:) Minterm: Dr. GANESHAPERUMAL DHARMARAJ ECE18R277 4/7 Karnaugh-Map(K-Map) Maxterm: A maxterm of n variables = sum of n literals in which each variable appears exactly once in T or F from, but not in both. Each maxterm has a value of 0 for exactly one combination of values of variables. E. g. A + B + C’ (001) = M1 (the value is 0). Therefore Mi = mi0 . A function can be written as a product of maxterms, which is referred to as a maxterm expansion or a standard product of sums Dr. GANESHAPERUMAL DHARMARAJ ECE18R277 5/7 Karnaugh-Map(K-Map) Maxterm Notation: f = (A+B+C)(A+B+C’)(A+B’+C) The other way to represent f is: 1 2 f (A,B,C) = M Q0 . M1 . M2 f (A,B,C) = M (0,1,2) Minterms present in f correspond with the 1’s of f in the truth table. Dr. GANESHAPERUMAL DHARMARAJ ECE18R277 6/7 Karnaugh-Map(K-Map Maxterm:) Minterm: Dr. GANESHAPERUMAL DHARMARAJ ECE18R277 7/7