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Online minimization of boolean functions



bin ( 6 ) 0111011111011111110010111100110101100100110100010111011110010010

Truth table
abcdefOutput
0 0 0 0 0 0 0
0 0 0 0 0 1 1
0 0 0 0 1 0 1
0 0 0 0 1 1 1
0 0 0 1 0 0 0
0 0 0 1 0 1 1
0 0 0 1 1 0 1
0 0 0 1 1 1 1
0 0 1 0 0 0 1
0 0 1 0 0 1 1
0 0 1 0 1 0 0
0 0 1 0 1 1 1
0 0 1 1 0 0 1
0 0 1 1 0 1 1
0 0 1 1 1 0 1
0 0 1 1 1 1 1
0 1 0 0 0 0 1
0 1 0 0 0 1 1
0 1 0 0 1 0 0
0 1 0 0 1 1 0
0 1 0 1 0 0 1
0 1 0 1 0 1 0
0 1 0 1 1 0 1
0 1 0 1 1 1 1
0 1 1 0 0 0 1
0 1 1 0 0 1 1
0 1 1 0 1 0 0
0 1 1 0 1 1 0
0 1 1 1 0 0 1
0 1 1 1 0 1 1
0 1 1 1 1 0 0
0 1 1 1 1 1 1
1 0 0 0 0 0 0
1 0 0 0 0 1 1
1 0 0 0 1 0 1
1 0 0 0 1 1 0
1 0 0 1 0 0 0
1 0 0 1 0 1 1
1 0 0 1 1 0 0
1 0 0 1 1 1 0
1 0 1 0 0 0 1
1 0 1 0 0 1 1
1 0 1 0 1 0 0
1 0 1 0 1 1 1
1 0 1 1 0 0 0
1 0 1 1 0 1 0
1 0 1 1 1 0 0
1 0 1 1 1 1 1
1 1 0 0 0 0 0
1 1 0 0 0 1 1
1 1 0 0 1 0 1
1 1 0 0 1 1 1
1 1 0 1 0 0 0
1 1 0 1 0 1 1
1 1 0 1 1 0 1
1 1 0 1 1 1 1
1 1 1 0 0 0 1
1 1 1 0 0 1 0
1 1 1 0 1 0 0
1 1 1 0 1 1 1
1 1 1 1 0 0 0
1 1 1 1 0 1 0
1 1 1 1 1 0 1
1 1 1 1 1 1 0

DNF (with ~) = ~a~b~c~d~ef + ~a~b~c~de~f + ~a~b~c~def + ~a~b~cd~ef + ~a~b~cde~f + ~a~b~cdef + ~a~bc~d~e~f + ~a~bc~d~ef + ~a~bc~def + ~a~bcd~e~f + ~a~bcd~ef + ~a~bcde~f + ~a~bcdef + ~ab~c~d~e~f + ~ab~c~d~ef + ~ab~cd~e~f + ~ab~cde~f + ~ab~cdef + ~abc~d~e~f + ~abc~d~ef + ~abcd~e~f + ~abcd~ef + ~abcdef + a~b~c~d~ef + a~b~c~de~f + a~b~cd~ef + a~bc~d~e~f + a~bc~d~ef + a~bc~def + a~bcdef + ab~c~d~ef + ab~c~de~f + ab~c~def + ab~cd~ef + ab~cde~f + ab~cdef + abc~d~e~f + abc~def + abcde~f

DNF (with overline) = abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef + abcdef

CNF (with ~) = (a + b + c + d + e + f) (a + b + c + ~d + e + f) (a + b + ~c + d + ~e + f) (a + ~b + c + d + ~e + f) (a + ~b + c + d + ~e + ~f) (a + ~b + c + ~d + e + ~f) (a + ~b + ~c + d + ~e + f) (a + ~b + ~c + d + ~e + ~f) (a + ~b + ~c + ~d + ~e + f) (~a + b + c + d + e + f) (~a + b + c + d + ~e + ~f) (~a + b + c + ~d + e + f) (~a + b + c + ~d + ~e + f) (~a + b + c + ~d + ~e + ~f) (~a + b + ~c + d + ~e + f) (~a + b + ~c + ~d + e + f) (~a + b + ~c + ~d + e + ~f) (~a + b + ~c + ~d + ~e + f) (~a + ~b + c + d + e + f) (~a + ~b + c + ~d + e + f) (~a + ~b + ~c + d + e + ~f) (~a + ~b + ~c + d + ~e + f) (~a + ~b + ~c + ~d + e + f) (~a + ~b + ~c + ~d + e + ~f) (~a + ~b + ~c + ~d + ~e + ~f)

CNF (with overline) = (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f) (a + b + c + d + e + f)

Some minimal forms exist.

Minimal Form (with ~) =

abde~f + c~d~e~f + ~bcef + b~cde + ~acdf + a~c~ef + ~a~bcd + ~ab~e~f + ~a~b~ce + ~b~d~ef + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + b~cde + ~acdf + a~c~ef + ~a~bcd + ~ab~e~f + ~bc~d~e + ~a~b~ce + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + b~cde + ~acdf + a~c~ef + ~a~bcd + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + b~cde + ~acdf + a~c~ef + ~a~bcd + ~ab~e~f + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + b~cde + ~acdf + a~c~ef + ~a~bcd + ~bc~df + ~ab~e~f + ~a~b~ce + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + b~cde + ~acdf + a~c~ef + ~a~bcd + ~bc~df + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~a~cde + ~ab~e~f + ~a~b~ce + ~b~d~ef + ~a~d~ef + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~a~cde + ~ab~e~f + ~a~b~ce + ~b~d~ef + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~a~cde + ~ab~e~f + ~bc~d~e + ~a~b~ce + ~a~d~ef + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~a~cde + ~ab~e~f + ~bc~d~e + ~a~b~ce + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~a~cde + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~a~cde + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~a~cde + ~ab~e~f + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~a~cde + ~ab~e~f + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~bc~df + ~a~cde + ~ab~e~f + ~a~b~ce + ~a~d~ef + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~bc~df + ~a~cde + ~ab~e~f + ~a~b~ce + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~bc~df + ~a~cde + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + ~acdf + ~a~bcd + ~bc~df + ~a~cde + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~ab~e~f + ~a~b~ce + ~b~d~ef + ~a~d~ef + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~ab~e~f + ~a~b~ce + ~b~d~ef + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~ab~e~f + ~bc~d~e + ~a~b~ce + ~a~d~ef + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~ab~e~f + ~bc~d~e + ~a~b~ce + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~ab~e~f + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~ab~e~f + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~bc~df + ~ab~e~f + ~a~b~ce + ~a~d~ef + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~bc~df + ~ab~e~f + ~a~b~ce + ~a~d~ef + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~bc~df + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~c~ef + ac~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ab~cf + b~cde + ~acdf + ~a~bcd + ~bc~df + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + b~cde + ~acdf + a~c~ef + ~a~bcd + ~ab~e~f + ~a~b~ce + ~b~d~ef + ~a~d~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + b~cde + ~acdf + a~c~ef + ~a~bcd + ~ab~e~f + ~bc~d~e + ~a~b~ce + ~a~d~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + b~cde + ~acdf + a~c~ef + ~a~bcd + ~ab~e~f + ~ab~d~e + ~a~b~ce + ~b~d~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + b~cde + ~acdf + a~c~ef + ~a~bcd + ~ab~e~f + ~ab~d~e + ~bc~d~e + ~a~b~ce + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + b~cde + ~acdf + a~c~ef + ~a~bcd + ~bc~df + ~ab~e~f + ~a~b~ce + ~a~d~ef + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + b~cde + ~acdf + a~c~ef + ~a~bcd + ~bc~df + ~ab~e~f + ~ab~d~e + ~a~b~ce + ab~def + a~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~a~cde + ~ab~e~f + ~b~d~ef + ~a~d~ef + ac~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~a~cde + ~ab~e~f + ~b~d~ef + ~a~d~ef + ab~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~a~cde + ~ab~e~f + ~bc~d~e + ~a~d~ef + ac~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~a~cde + ~ab~e~f + ~bc~d~e + ~a~d~ef + ab~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~a~cde + ~ab~e~f + ~ab~d~e + ~b~d~ef + ac~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~a~cde + ~ab~e~f + ~ab~d~e + ~b~d~ef + ab~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~a~cde + ~ab~e~f + ~ab~d~e + ~bc~d~e + ac~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~a~cde + ~ab~e~f + ~ab~d~e + ~bc~d~e + ab~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~bc~df + ~a~cde + ~ab~e~f + ~a~d~ef + ac~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~bc~df + ~a~cde + ~ab~e~f + ~a~d~ef + ab~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~bc~df + ~a~cde + ~ab~e~f + ~ab~d~e + ac~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~a~bf + ab~ce + ~acdf + a~c~ef + ~a~bcd + ~bc~df + ~a~cde + ~ab~e~f + ~ab~d~e + ab~def + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bde + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ac~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bde + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ab~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bde + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ac~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bde + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~bc~df + ~a~bde + ~ab~d~e + ~a~b~ce + ~b~c~ef + ac~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~bc~df + ~a~bde + ~ab~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bcd + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ac~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bcd + ~ab~d~e + ~a~b~ce + ~b~d~ef + ~b~c~ef + ab~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bcd + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ac~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bcd + ~ab~d~e + ~bc~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bcd + ~bc~df + ~ab~d~e + ~a~b~ce + ~b~c~ef + ac~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ab~cf + ~adef + ~a~bcd + ~bc~df + ~ab~d~e + ~a~b~ce + ~b~c~ef + ab~def + a~c~de~f + ~ab~cd~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ~a~bf + ab~ce + ~adef + a~c~ef + ~a~bde + ~ab~d~e + ~b~d~ef + ac~def + ~ab~cd~f + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ~a~bf + ab~ce + ~adef + a~c~ef + ~a~bde + ~ab~d~e + ~b~d~ef + ab~def + ~ab~cd~f + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ~a~bf + ab~ce + ~adef + a~c~ef + ~a~bde + ~ab~d~e + ~bc~d~e + ac~def + ~ab~cd~f + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ~a~bf + ab~ce + ~adef + a~c~ef + ~a~bde + ~ab~d~e + ~bc~d~e + ab~def + ~ab~cd~f + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ~a~bf + ab~ce + ~adef + a~c~ef + ~bc~df + ~a~bde + ~ab~d~e + ac~def + ~ab~cd~f + ~b~c~de~f

abde~f + c~d~e~f + ~bcef + ~ac~e + ~a~bf + ab~ce + ~adef + a~c~ef + ~bc~df + ~a~bde + ~ab~d~e + ab~def + ~ab~cd~f + ~b~c~de~f


Minimal Form (with overline) =

abdef + cdef + bcef + bcde + acdf + acef + abcd + abef + abce + bdef + adef + bcef + abdef + acdef

abdef + cdef + bcef + bcde + acdf + acef + abcd + abef + bcde + abce + adef + bcef + abdef + acdef

abdef + cdef + bcef + bcde + acdf + acef + abcd + abef + abde + abce + bdef + bcef + abdef + acdef

abdef + cdef + bcef + bcde + acdf + acef + abcd + abef + abde + bcde + abce + bcef + abdef + acdef

abdef + cdef + bcef + bcde + acdf + acef + abcd + bcdf + abef + abce + adef + bcef + abdef + acdef

abdef + cdef + bcef + bcde + acdf + acef + abcd + bcdf + abef + abde + abce + bcef + abdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + acde + abef + abce + bdef + adef + bcef + acdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + acde + abef + abce + bdef + adef + bcef + abdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + acde + abef + bcde + abce + adef + bcef + acdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + acde + abef + bcde + abce + adef + bcef + abdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + acde + abef + abde + abce + bdef + bcef + acdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + acde + abef + abde + abce + bdef + bcef + abdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + acde + abef + abde + bcde + abce + bcef + acdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + acde + abef + abde + bcde + abce + bcef + abdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + bcdf + acde + abef + abce + adef + bcef + acdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + bcdf + acde + abef + abce + adef + bcef + abdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + bcdf + acde + abef + abde + abce + bcef + acdef + acdef

abdef + cdef + bcef + abcf + acdf + abcd + bcdf + acde + abef + abde + abce + bcef + abdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + abef + abce + bdef + adef + bcef + acdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + abef + abce + bdef + adef + bcef + abdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + abef + bcde + abce + adef + bcef + acdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + abef + bcde + abce + adef + bcef + abdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + abef + abde + abce + bdef + bcef + acdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + abef + abde + abce + bdef + bcef + abdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + abef + abde + bcde + abce + bcef + acdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + abef + abde + bcde + abce + bcef + abdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + bcdf + abef + abce + adef + bcef + acdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + bcdf + abef + abce + adef + bcef + abdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + bcdf + abef + abde + abce + bcef + acdef + acdef

abdef + cdef + bcef + abcf + bcde + acdf + abcd + bcdf + abef + abde + abce + bcef + abdef + acdef

abdef + cdef + bcef + abf + bcde + acdf + acef + abcd + abef + abce + bdef + adef + abdef + acdef

abdef + cdef + bcef + abf + bcde + acdf + acef + abcd + abef + bcde + abce + adef + abdef + acdef

abdef + cdef + bcef + abf + bcde + acdf + acef + abcd + abef + abde + abce + bdef + abdef + acdef

abdef + cdef + bcef + abf + bcde + acdf + acef + abcd + abef + abde + bcde + abce + abdef + acdef

abdef + cdef + bcef + abf + bcde + acdf + acef + abcd + bcdf + abef + abce + adef + abdef + acdef

abdef + cdef + bcef + abf + bcde + acdf + acef + abcd + bcdf + abef + abde + abce + abdef + acdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + acde + abef + bdef + adef + acdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + acde + abef + bdef + adef + abdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + acde + abef + bcde + adef + acdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + acde + abef + bcde + adef + abdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + acde + abef + abde + bdef + acdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + acde + abef + abde + bdef + abdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + acde + abef + abde + bcde + acdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + acde + abef + abde + bcde + abdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + bcdf + acde + abef + adef + acdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + bcdf + acde + abef + adef + abdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + bcdf + acde + abef + abde + acdef + bcdef

abdef + cdef + bcef + abf + abce + acdf + acef + abcd + bcdf + acde + abef + abde + abdef + bcdef

abdef + cdef + bcef + ace + abcf + adef + abde + abde + abce + bdef + bcef + acdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abde + abde + abce + bdef + bcef + abdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abde + abde + bcde + abce + bcef + acdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abde + abde + bcde + abce + bcef + abdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + bcdf + abde + abde + abce + bcef + acdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + bcdf + abde + abde + abce + bcef + abdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abcd + abde + abce + bdef + bcef + acdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abcd + abde + abce + bdef + bcef + abdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abcd + abde + bcde + abce + bcef + acdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abcd + abde + bcde + abce + bcef + abdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abcd + bcdf + abde + abce + bcef + acdef + acdef + abcdf

abdef + cdef + bcef + ace + abcf + adef + abcd + bcdf + abde + abce + bcef + abdef + acdef + abcdf

abdef + cdef + bcef + ace + abf + abce + adef + acef + abde + abde + bdef + acdef + abcdf + bcdef

abdef + cdef + bcef + ace + abf + abce + adef + acef + abde + abde + bdef + abdef + abcdf + bcdef

abdef + cdef + bcef + ace + abf + abce + adef + acef + abde + abde + bcde + acdef + abcdf + bcdef

abdef + cdef + bcef + ace + abf + abce + adef + acef + abde + abde + bcde + abdef + abcdf + bcdef

abdef + cdef + bcef + ace + abf + abce + adef + acef + bcdf + abde + abde + acdef + abcdf + bcdef

abdef + cdef + bcef + ace + abf + abce + adef + acef + bcdf + abde + abde + abdef + abcdf + bcdef






Karnaugh map ab

ef ef ef ef
cd 0 1 1 1
cd 0 1 1 1
cd 1 1 1 1
cd 1 1 1 0

Karnaugh map ab

ef ef ef ef
cd 1 1 0 0
cd 1 0 1 1
cd 1 1 1 0
cd 1 1 0 0

Karnaugh map ab

ef ef ef ef
cd 0 1 1 1
cd 0 1 1 1
cd 0 0 0 1
cd 1 0 1 0

Karnaugh map ab

ef ef ef ef
cd 0 1 0 1
cd 0 1 0 0
cd 0 0 1 0
cd 1 1 1 0