Karnaugh maps are a method for simplifying Boolean algebra expressions. They allow visualizing the relationships between variables in a logic circuit to minimize logic expressions into their simplest disjunctive normal form (Sum of Products) or conjunctive normal form (Product of Sum). The document provides an example of a 4-variable Karnaugh map and simplifies the logic expression into its minimal form. In summary, Karnaugh maps are a graphical technique for simplifying logic expressions into their minimal sum-of-products or product-of-sums form.

1. ldfkda is;shï
Karnaugh Maps
ufyaIa fldä;=jlal=
BTec(UG) , MCTS, MIEEE
Professional Development Course in ICT (AIT-Thailand)
National Dip in Teaching (Merit)

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ir, lrkak
A B + A B + AB + AB

3. .=Ks;fha tl;=j yd tl;=fõ .=Ks;h
Sum of Product (SOP) and
Product of Sum (POS)

4. A B C Out Put
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
.=Ks;fha tl;=j Sum of Product (SOP)
A’.B’.C’
A’.B’.C
A.B’.C’
A.B.C’

5. A’.B’.C’ A’.B’.C A.B’.C’ A.B.C’+ + +
A B C Out Put
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
.=Ks;fha tl;=j Sum of Product (SOP)
A’.B’.C’
A’.B’.C
A.B’.C’
A.B.C’

6. tl;=fõ .=Ks;h Product of Sum (POS)
A B C Out Put
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
A + B’ + C
A + B’ + C’
A’ + B + C’
A’ + B’ + C’

7. tl;=fõ .=Ks;h Product of Sum (POS)
A B C Out Put
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
A + B’ + C
A + B’ + C’
A’ + B + C’
A’ + B’ + C’
(A + B’ + C). (A + B’ + C’). (A’ + B + C’). (A’ + B’ + C’)

8. ldfkda is;shï Karnaugh Maps
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y÷kajd fok ,oS'

10. A B + A B + AB + AB
A B
A B
A B
A B
A B
0
1
0 1
1
1 1
AB + A + B

11. oeka my; .eg,qj úi|k wdldrh n,uq
X Y Out put
0 0 1
0 1 1
1 0 0
1 1 0

12. X Y Out
put
0 0 1
0 1 1
1 0 0
1 1 0
X
Y
0
1
0 1
1 1
X Y
X Y

13. wdodk 4 la iys; wjia:d

14. A B C D Out put
(X)
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 1
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 1
1 1 1 0 0
1 1 1 1 1
A’B’C’D’
A’BC’D
A’BCD
ABC’D
ABCD

15. AB
CD
00
01
11
10
00 01 11 10
1
1 1
1 1

16. A’B’C’D’ + A’B’CD’ + AB’C’D’ + AB’CD’
AB
CD
00
01
11
10
00 01 11 10
1 1
1 1

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tu nQ,shdkq ùc .Ks;uh iólrK ldfkda
is;shï weiqßka iqtlrkak

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