digital electronics- minimization techniquekarnaugh map

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New

Delhi-75Affiliated Institution of G.G.S.IP.U, Delhi

DIGITAL ELECTRONICSPaper Code :- BCA 106

Keywords:Boolean Algebra, logic, K-Map

By :-HARI MOHAN JAIN

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

2

Minimization TechniqueKarnaugh

Map

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

3Karnaugh Map (K Map)

• 2 Variable K Map

• 3 Variable K Map

• 4 Variable K Map

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

42 Variable Karnaugh map.

a b f (a,b)0 00 11 01 1

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

5K-map for f(a, b) = ab + ab’.

a b f (a,b)0 0 00 1 01 0 11 1 1

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

6K-map solution for f(a, b) = ab + ab’.

a b f (a,b)0 0 00 1 01 0 11 1 1

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

7K-map solution for f(a, b) = ab + ab’ + a’b’.

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

K-map solution for f(a, b) = ab’ + a’b.

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

3 Variable K Map

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

3 variable K-map

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

K-map solution for Equation ab’c’+ab’c+abc+a’b’c+a’bc+a’bc’

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 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

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 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

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75 14

Solution of Equationf(a,b,c) = a’bc+ab’c’+abc+abc’

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

4 Variable Karnaugh mapa b c d f (a,b,c,d)0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 1

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 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 10 0 0 1 00 0 1 0 10 0 1 1 00 1 0 0 00 1 0 1 00 1 1 0 00 1 1 1 01 0 0 0 11 0 0 1 11 0 1 0 11 0 1 1 11 1 0 0 11 1 0 1 11 1 1 0 11 1 1 1 1

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

K-map with don’t caresa b c d f (a,b,c,d)0 0 0 0 00 0 0 1 00 0 1 0 00 0 1 1 10 1 0 0 10 1 0 1 X0 1 1 0 00 1 1 1 11 0 0 0 01 0 0 1 X1 0 1 0 11 0 1 1 01 1 0 0 01 1 0 1 11 1 1 0 01 1 1 1 X