digital electronics- minimization techniquekarnaugh map
TRANSCRIPT
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