DIGITAL ELECTRONICS- Minimization TechniqueKarnaugh Map 4 Variable K Map 2 Variable K Map 3 Variable K Map K-map solution for Equation K-map for Equation

1. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Affiliated Institution of G.G.S.IP.U, Delhi
DIGITAL ELECTRONICS
Paper Code :- BCA 106
Keywords:
Boolean Algebra, logic, K-Map
By :-HARI MOHAN JAIN

2. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
2
Minimization
Technique
Karnaugh Map

3. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
3
Karnaugh Map (K Map)
• 2 Variable K Map
• 3 Variable K Map
• 4 Variable K Map

4. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
4
2 Variable Karnaugh map.
a b f (a,b)
0 0
0 1
1 0
1 1

5. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
5
K-map for f(a, b) = ab + ab’.
a b f (a,b)
0 0 0
0 1 0
1 0 1
1 1 1

6. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
6
K-map solution for f(a, b) = ab + ab’.
a b f (a,b)
0 0 0
0 1 0
1 0 1
1 1 1

7. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
7
K-map solution for f(a, b) = ab + ab’ + a’b’.

8. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
K-map solution for f(a, b) = ab’ + a’b.

9. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
3 Variable K Map

10. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
3 variable K-map

11. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
K-map solution for Equation
ab’c’+ab’c+abc+a’b’c+a’bc+a’bc’

12. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
K-map for Equation
f(x,y,z) = x’y’z’+x’y’z+x’yz+xy’z

13. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
K-map for Equation
f(x,y,z) = x’y’z’+x’y’z+x’yz+xy’z

14. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
14
Solution of Equation
f(a,b,c) = a’bc+ab’c’+abc+abc’

15. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
4 Variable Karnaugh map
a b c d f (a,b,c,d)
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1

16. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
f(a,b,c,d) =
a’b’c’d’+a’b’cd’+abc’d’+abc’d+abcd+abcd’+ab’c’d’+ab’c’d+ab’cd+ab’cd’
a b c d f (a,b,c,d)
0 0 0 0 1
0 0 0 1 0
0 0 1 0 1
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 1
1 0 0 1 1
1 0 1 0 1
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1

17. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
K-map with don’t cares
a b c d f (a,b,c,d)
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 1
0 1 0 1 X
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 X
1 0 1 0 1
1 0 1 1 0
1 1 0 0 0
1 1 0 1 1
1 1 1 0 0
1 1 1 1 X