Home   Online minimization of boolean functions


Karnaugh map gallery

Truth table is same. But minimal forms have no common term.

3 Input example

Calc
Karnaugh map

c c
ab 1 1
ab 0 1
ab 1 1
ab 1 0


c c
ab 1 1
ab 0 1
ab 1 1
ab 1 0

Minimal Form (with ~) =

bc + a~c + ~a~b

ab + ~ac + ~b~c


Minimal Form (with overline) =

bc + ac + ab

ab + ac + bc



4 Input example(1)

Calc
Karnaugh map

cd cd cd cd
ab 0 0 0 0
ab 0 1 1 1
ab 0 1 0 1
ab 0 1 1 1


cd cd cd cd
ab 0 0 0 0
ab 0 1 1 1
ab 0 1 0 1
ab 0 1 1 1

Minimal Form (with ~) =

a~bc + a~cd + bc~d + ~abd

ac~d + a~bd + ~abc + b~cd


Minimal Form (with overline) =

abc + acd + bcd + abd

acd + abd + abc + bcd



4 Input example(2)

Calc
Karnaugh map

cd cd cd cd
ab 1 0 1 1
ab 1 1 1 0
ab 0 1 1 1
ab 1 1 0 1


cd cd cd cd
ab 1 0 1 1
ab 1 1 1 0
ab 0 1 1 1
ab 1 1 0 1

Minimal Form (with ~) =

~b~d + abc + a~cd + ~acd + ~ab~c

bd + ac~d + a~b~c + ~a~bc + ~a~c~d


Minimal Form (with overline) =

bd + abc + acd + acd + abc

bd + acd + abc + abc + acd