# k map 1 ```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
```