Home Online minimization of boolean functions Tweet
a | b | c | d | e | f | Output |
---|---|---|---|---|---|---|
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 |
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
ef | ef | ef | ef | |
---|---|---|---|---|
cd | 0 | 1 | 1 | 1 |
cd | 0 | 1 | 1 | 1 |
cd | 1 | 1 | 1 | 1 |
cd | 1 | 1 | 1 | 0 |
ef | ef | ef | ef | |
---|---|---|---|---|
cd | 1 | 1 | 0 | 0 |
cd | 1 | 0 | 1 | 1 |
cd | 1 | 1 | 1 | 0 |
cd | 1 | 1 | 0 | 0 |
ef | ef | ef | ef | |
---|---|---|---|---|
cd | 0 | 1 | 1 | 1 |
cd | 0 | 1 | 1 | 1 |
cd | 0 | 0 | 0 | 1 |
cd | 1 | 0 | 1 | 0 |
ef | ef | ef | ef | |
---|---|---|---|---|
cd | 0 | 1 | 0 | 1 |
cd | 0 | 1 | 0 | 0 |
cd | 0 | 0 | 1 | 0 |
cd | 1 | 1 | 1 | 0 |