Mapa de Karnaugh frente a Quine–McCluskey
Un mapa de Karnaugh y el método de Quine–McCluskey encuentran lo mismo, los implicantes primos de una función y una cobertura hecha con ellos; el mapa lo hace a ojo con hasta cuatro o cinco variables, el método tabular lo hace mecánicamente para cualquier número. La función de diez mintérminos de abajo tiene seis implicantes primos y una cobertura de tres términos.
La función es Σm(A, B, C, D; 0, 1, 2, 5, 6, 7, 8, 9, 10, 14), un ejemplo de libro. El mapa del motor informa de seis implicantes primos y obtiene la cobertura (NOT A AND B AND D) OR (NOT B AND NOT C) OR (C AND NOT D), tres términos, comprobada equivalente en las dieciséis filas. La FND canónica tiene diez términos y la FNC canónica seis cláusulas, y la construcción mecánica de compuertas a partir de la forma canónica llega a cientos de compuertas en cualquiera de las dos bases, y por eso nadie construye a partir de la forma canónica.
Quine–McCluskey encuentra los mismos seis implicantes primos fusionando repetidamente mintérminos que difieren en un bit, en una tabla en lugar de una cuadrícula, y después selecciona una cobertura a partir de una tabla de implicantes primos, donde los implicantes esenciales se eligen primero. El mapa hace la fusión visualmente, con la continuidad por los bordes en el papel de la regla de diferencia de un bit. Más allá de cuatro variables la cuadrícula deja de ser legible y la tabla sigue funcionando, con coste exponencial en el peor caso; esa es toda la comparativa.
El conversor a formas normales del motor tiene un método de implicantes primos al que recurre cuando la ruta algebraica supera sus límites, que es la idea tabular aplicada por máquina. Ni el mapa ni la tabla afirman que su cobertura sea la más pequeña entre varias irreducibles; el motor llama irreducible a su cobertura y la comprueba, sin afirmar que sea la más pequeña posible.
Ejemplo
f := Σm(A, B, C, D; 0, 1, 2, 5, 6, 7, 8, 9, 10, 14) · salida
Comprobaciones exactas
¿Siempre verdadera (tautología)? No Contraejemplo: A = F, B = F, C = V, D = V · Exhaustively checked and solver cross-checked · 4 filas
¿Siempre falsa (contradicción)? No Contraejemplo: A = F, B = F, C = F, D = F · Exhaustively checked and solver cross-checked · 1 filas
¿Puede ser verdadera? Sí Asignación de ejemplo: A = F, B = F, C = F, D = F · Exhaustively checked and solver cross-checked · 1 filas
Tabla de verdad (16 filas)
| # | A | B | C | D | f |
|---|---|---|---|---|---|
| 0 | FALSO | FALSO | FALSO | FALSO | VERDADERO |
| 1 | FALSO | FALSO | FALSO | VERDADERO | VERDADERO |
| 2 | FALSO | FALSO | VERDADERO | FALSO | VERDADERO |
| 3 | FALSO | FALSO | VERDADERO | VERDADERO | FALSO |
| 4 | FALSO | VERDADERO | FALSO | FALSO | FALSO |
| 5 | FALSO | VERDADERO | FALSO | VERDADERO | VERDADERO |
| 6 | FALSO | VERDADERO | VERDADERO | FALSO | VERDADERO |
| 7 | FALSO | VERDADERO | VERDADERO | VERDADERO | VERDADERO |
| 8 | VERDADERO | FALSO | FALSO | FALSO | VERDADERO |
| 9 | VERDADERO | FALSO | FALSO | VERDADERO | VERDADERO |
| 10 | VERDADERO | FALSO | VERDADERO | FALSO | VERDADERO |
| 11 | VERDADERO | FALSO | VERDADERO | VERDADERO | FALSO |
| 12 | VERDADERO | VERDADERO | FALSO | FALSO | FALSO |
| 13 | VERDADERO | VERDADERO | FALSO | VERDADERO | FALSO |
| 14 | VERDADERO | VERDADERO | VERDADERO | FALSO | VERDADERO |
| 15 | VERDADERO | VERDADERO | VERDADERO | VERDADERO | FALSO |
Diagrama lógico
Mapa de Karnaugh
AB \ CD
00
01
11
10
00
1m0
1m1
0m3
1m2
01
0m4
1m5
1m7
1m6
11
0m12
0m13
0m15
1m14
10
1m8
1m9
0m11
1m10
- celdas m5, m7
NOT A AND B AND D - celdas m0, m1, m8, m9
NOT B AND NOT C - celdas m2, m6, m10, m14
C AND NOT D
(NOT A AND B AND D) OR (NOT B AND NOT C) OR (C AND NOT D) · Derived (NOT A AND B AND D) OR (NOT B AND NOT C) OR (C AND NOT D). Exactly equivalent on every assignment.
Mintérminos y maxtérminos
f(A, B, C, D) = Σm(0, 1, 2, 5, 6, 7, 8, 9, 10, 14)f(A, B, C, D) = ΠM(3, 4, 11, 12, 13, 15)Orden de variables: A, B, C, D · 16 filas
Formas normales
Forma normal conjuntiva (FNC)
(A OR B OR NOT C OR NOT D) AND (A OR NOT B OR C OR D) AND (NOT A OR B OR NOT C OR NOT D) AND (NOT A OR NOT B OR C OR D) AND (NOT A OR NOT B OR C OR NOT D) AND (NOT A OR NOT B OR NOT C OR NOT D)6 cláusulas, 24 literales · complete · Desarrollo en mintérminos ×1
Forma normal disyuntiva (FND)
(A AND B AND C AND NOT D) OR (A AND NOT B AND C AND NOT D) OR (A AND NOT B AND NOT C AND D) OR (A AND NOT B AND NOT C AND NOT D) OR (NOT A AND B AND C AND D) OR (NOT A AND B AND C AND NOT D) OR (NOT A AND B AND NOT C AND D) OR (NOT A AND NOT B AND C AND NOT D) OR (NOT A AND NOT B AND NOT C AND D) OR (NOT A AND NOT B AND NOT C AND NOT D)10 términos, 40 literales · complete · Desarrollo en mintérminos ×1
Solo NAND, solo NOR
Forma solo con NAND
NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D)))), NAND(NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D))))), NAND(NAND(NAND(NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D)))), NAND(NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D)))))), NAND(NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))), NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D))))), NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))), NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D))))))), NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D)))), NAND(NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D))))), NAND(NAND(NAND(NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D)))), NAND(NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))))), NAND(NAND(NAND(NAND(A, A), NAND(B, B)), NAND(NAND(A, A), NAND(B, B))), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D)))))), NAND(NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))), NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D))))), NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))), NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D)))))))), NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, D), NAND(C, D))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D))))), NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, D), NAND(C, D))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D)))), NAND(NAND(NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, D), NAND(C, D))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D))))), NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, D), NAND(C, D))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))))), NAND(NAND(NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D)))), NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D))))), NAND(NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D)))), NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D))))))), NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, D), NAND(C, D))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D))))), NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, D), NAND(C, D))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D)))), NAND(NAND(NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, D), NAND(C, D))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D))))), NAND(NAND(NAND(NAND(NAND(A, A), B), NAND(NAND(A, A), B)), NAND(NAND(C, D), NAND(C, D))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), NAND(D, D)), NAND(NAND(C, C), NAND(D, D)))))), NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))))), NAND(NAND(NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D)))), NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D))))), NAND(NAND(NAND(NAND(A, NAND(B, B)), NAND(A, NAND(B, B))), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D)))), NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(C, NAND(D, D)), NAND(C, NAND(D, D)))))))))719 compuertas · equivalencia verificada en todas las filas
Forma solo con NOR
NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))))), NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))))), NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))))), NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))))))), NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D))))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D))))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))))), NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D))))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D))))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))))))), NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))))), NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))))), NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, D), NOR(C, D))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(A, B), NOR(A, B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))))), NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))))))), NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D))))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D))))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))))), NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D))))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D))))), NOR(NOR(NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D)))), NOR(NOR(NOR(NOR(A, NOR(B, B)), NOR(A, NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, D), NOR(C, D))))), NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))))), NOR(NOR(NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(NOR(NOR(NOR(NOR(A, A), B), NOR(NOR(A, A), B)), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), D), NOR(NOR(C, C), D)))))))))1247 compuertas · equivalencia verificada en todas las filas
El error habitual
Leer un mapa sin ver la continuidad por los bordes. Las celdas 0, 2, 8 y 10 de un mapa de cuatro variables son las cuatro esquinas, un solo grupo, NOT B AND NOT D; quien las ve como dos pares separados escribe una cobertura más larga y nada está mal salvo la longitud.
Preguntas
¿Cuándo debería dejar de usar el mapa?
Con cinco variables el mapa se convierte en dos mapas de cuatro variables lado a lado, y con seis es ilegible. El motor dibuja mapas hasta cuatro variables y usa el método de implicantes primos más allá.
¿La cobertura de tres términos es la única?
No necesariamente; con seis implicantes primos y tres en la cobertura, otra selección puede cubrir los mismos mintérminos con el mismo recuento. El motor informa de una cobertura y la comprueba; cuál es la más barata depende de la tecnología.
Relacionado
Ejercicios
- Ejercicios de mapas de Karnaugh, 2 variables
- Ejercicios de mapas de Karnaugh, 3 variables
- Ejercicios de mapas de Karnaugh, 4 variables
Véase también
- Mapa de Karnaugh: definición, ejemplo y equivalente en inglés
- Método de Quine–McCluskey: definición, ejemplo y equivalente en inglés
- Implicante primo: definición, ejemplo y equivalente en inglés
- Implicante primo esencial: definición, ejemplo y equivalente en inglés
- Solucionador de mapas de Karnaugh: de 2 a 4 variables, agrupaciones, SOP y POS
- Implicantes primos e implicantes primos esenciales en un mapa de Karnaugh
- Regla de agrupación en el mapa de Karnaugh: las celdas adyacentes eliminan la variable que cambia
- Lección 11: Mapas de Karnaugh
Comparar
Generado a partir del motor de Tangibool, semántica tangibool-semantics/1, motor 1.0.0, compilación . Cada tabla, mapa, simplificación y veredicto de estas páginas lo calculó el motor de Tangibool al compilar el sitio, y cada afirmación la volvió a comprobar el mismo verificador exacto que usa la app. Los límites se indican donde aplican. © 2026 Foreranger LTD.