Solucionador de mapas de Karnaugh: de 2 a 4 variables, agrupaciones, SOP y POS
Dibuja el mapa de Karnaugh de una expresión con de dos a cuatro variables, mira las agrupaciones que sugiere el motor y lee la suma de productos derivada con una comprobación exacta de equivalencia.
Escribe una expresión (o una lista de mintérminos como Σm(A, B, C, D; 0, 2, 5, 7, 8, 10, 13, 15)) y la herramienta dispone el mapa con etiquetas de filas y columnas en código Gray, rellena cada celda con la evaluación del motor y sugiere una cobertura: rectángulos de 1, 2, 4, 8 o 16 celdas, con continuidad por los bordes, cada uno convertido en un término producto al eliminar la variable que cambia dentro del rectángulo. La expresión derivada se comprueba contra la original en todas las asignaciones.
El mapa muestra como máximo cuatro variables efectivas, que es el límite documentado del motor y el límite de lo que un mapa puede mostrar sin una tercera dimensión. Con más variables la herramienta lo dice, y la app te deja fijar entradas para ver un corte etiquetado explícitamente. Filas y columnas usan el orden en código Gray 00, 01, 11, 10, de modo que las celdas adyacentes difieren en una variable; el índice de mintérmino de cada celda está impreso en su esquina.
Si tu regla lleva supuestos que excluyen algunas entradas (un dígito BCD nunca supera 9, por ejemplo), marca la opción de indiferencias: las celdas a las que no llega ninguna asignación admisible se marcan con X y pueden cubrirse o no, y la expresión derivada es entonces equivalente dentro de los supuestos, cosa que la etiqueta indica.
Límites
- Tablas de verdad hasta 12 entradas (4096 filas).
- Mapas de Karnaugh hasta 4 variables efectivas.
- Formas normales hasta 4096 términos; expresiones hasta 20000 caracteres y 64 entradas.
Cómo escribir expresiones
Escribe las entradas como nombres (socio, A, credito_ok) y combínalas con AND, OR, NOT, XOR, -> (implica), <-> (si y solo si), NAND(a, b), NOR(a, b), XNOR(a, b), o los símbolos &&, ||, !, ∧, ∨, ¬, ·, +, ′. También funcionan las formas de mintérminos y maxtérminos: Σm(A, B, C; 1, 3), ΠM(A, B; 0). Precedencia: NOT, luego AND, luego XOR, luego OR, luego ->, luego <->; usa paréntesis para ser explícito. =, ==, ^, &, | y ~ se rechazan con una corrección.
Ejemplo
f := Σm(A, B, C, D; 0, 2, 5, 7, 8, 10, 13, 15) · salida
Comprobaciones exactas
Tabla de verdad (16 filas)
| # | A | B | C | D | f |
|---|---|---|---|---|---|
| 0 | FALSO | FALSO | FALSO | FALSO | VERDADERO |
| 1 | FALSO | FALSO | FALSO | VERDADERO | FALSO |
| 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 | FALSO |
| 7 | FALSO | VERDADERO | VERDADERO | VERDADERO | VERDADERO |
| 8 | VERDADERO | FALSO | FALSO | FALSO | VERDADERO |
| 9 | VERDADERO | FALSO | FALSO | VERDADERO | FALSO |
| 10 | VERDADERO | FALSO | VERDADERO | FALSO | VERDADERO |
| 11 | VERDADERO | FALSO | VERDADERO | VERDADERO | FALSO |
| 12 | VERDADERO | VERDADERO | FALSO | FALSO | FALSO |
| 13 | VERDADERO | VERDADERO | FALSO | VERDADERO | VERDADERO |
| 14 | VERDADERO | VERDADERO | VERDADERO | FALSO | FALSO |
| 15 | VERDADERO | VERDADERO | VERDADERO | VERDADERO | VERDADERO |
Lectura en lenguaje claro
Principiantef es verdadero exactamente cuando la fila de la tabla de verdad de (A, B, C, D) es una de las filas 0, 2, 5, 7, 8, 10, 13 y 15.
En todos los demás casos, f es falso.
Sobre los operadores:
- Σm enumera las filas de la tabla de verdad (mintérminos) en las que la fórmula es verdadera. Las filas se numeran desde 0 y la primera entrada indicada es el bit más significativo.
Intermediof es verdadero exactamente cuando la fila de la tabla de verdad de (A, B, C, D) es una de las filas 0, 2, 5, 7, 8, 10, 13 y 15.
En todos los demás casos, f es falso.
Avanzadof es verdadero exactamente cuando la fila de la tabla de verdad de (A, B, C, D) es una de las filas 0, 2, 5, 7, 8, 10, 13 y 15 [suma canónica de mintérminos (FND)].
En todos los demás casos, f es falso.
Notación formal: Σm(A, B, C, D; 0, 2, 5, 7, 8, 10, 13, 15)
Diagrama lógico
Simplificación paso a paso
El motor no encontró ninguna ley que acorte esta expresión; ya es tan corta como sus leyes de reescritura permiten.
Σm(A, B, C, D; 0, 2, 5, 7, 8, 10, 13, 15)
Mapa de Karnaugh
- celdas m0, m2, m8, m10
NOT B AND NOT D - celdas m5, m7, m13, m15
B AND D
Mintérminos y maxtérminos
f(A, B, C, D) = Σm(0, 2, 5, 7, 8, 10, 13, 15)f(A, B, C, D) = ΠM(1, 3, 4, 6, 9, 11, 12, 14)Orden de variables: A, B, C, D · 16 filas
Formas normales
Forma normal conjuntiva (FNC)
(A OR B OR C OR NOT D) AND (A OR B OR NOT C OR NOT D) AND (A OR NOT B OR C OR D) AND (A OR NOT B OR NOT C OR D) AND (NOT A OR B OR C OR NOT 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 NOT C OR D)8 cláusulas, 32 literales · complete · Desarrollo en mintérminos ×1
Forma normal disyuntiva (FND)
(A AND B AND C AND D) OR (A AND B AND NOT C AND D) OR (A AND NOT B AND C AND NOT 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 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 NOT D)8 términos, 32 literales · complete · Desarrollo en mintérminos ×1
Solo NAND, solo NOR
Forma solo con 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(C, NAND(D, D)), NAND(C, NAND(D, 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(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, D), NAND(C, 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, D), NAND(C, 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(C, NAND(D, D)), NAND(C, NAND(D, 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(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, D), NAND(C, 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, D), NAND(C, D))))))), NAND(NAND(NAND(NAND(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(C, NAND(D, D)), NAND(C, NAND(D, D))))), NAND(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(C, NAND(D, D)), NAND(C, NAND(D, D)))))), NAND(NAND(NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))), NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(C, D), NAND(C, D)))), NAND(NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))), NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(C, D), NAND(C, D)))))), NAND(NAND(NAND(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(C, NAND(D, D)), NAND(C, NAND(D, D))))), NAND(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(C, NAND(D, D)), NAND(C, NAND(D, D)))))), NAND(NAND(NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))), NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(C, D), NAND(C, D)))), NAND(NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(NAND(C, C), D), NAND(NAND(C, C), D))), NAND(NAND(NAND(A, B), NAND(A, B)), NAND(NAND(C, D), NAND(C, D))))))))383 compuertas · equivalencia verificada en todas las filas
Forma solo con 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(NOR(C, C), D), NOR(NOR(C, C), 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(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), NOR(D, D)), NOR(NOR(C, C), NOR(D, 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), NOR(D, D)), NOR(NOR(C, C), NOR(D, 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(NOR(C, C), D), NOR(NOR(C, C), 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(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), NOR(D, D)), NOR(NOR(C, C), NOR(D, 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), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))))))), NOR(NOR(NOR(NOR(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(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(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(NOR(C, C), D), NOR(NOR(C, C), D))))), NOR(NOR(NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D))))), NOR(NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D))))))), NOR(NOR(NOR(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(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(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(NOR(C, C), D), NOR(NOR(C, C), D))))), NOR(NOR(NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D))))), NOR(NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, 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(NOR(C, C), D), NOR(NOR(C, C), 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(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), NOR(D, D)), NOR(NOR(C, C), NOR(D, 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), NOR(D, D)), NOR(NOR(C, C), NOR(D, 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(NOR(C, C), D), NOR(NOR(C, C), 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(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), NOR(D, D)), NOR(NOR(C, C), NOR(D, 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), NOR(D, D)), NOR(NOR(C, C), NOR(D, D)))))))), NOR(NOR(NOR(NOR(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(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(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(NOR(C, C), D), NOR(NOR(C, C), D))))), NOR(NOR(NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D))))), NOR(NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D))))))), NOR(NOR(NOR(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(NOR(C, C), D), NOR(NOR(C, C), D)))), NOR(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(NOR(C, C), D), NOR(NOR(C, C), D))))), NOR(NOR(NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D))))), NOR(NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(C, NOR(D, D)), NOR(C, NOR(D, D)))), NOR(NOR(NOR(NOR(A, A), NOR(B, B)), NOR(NOR(A, A), NOR(B, B))), NOR(NOR(NOR(C, C), NOR(D, D)), NOR(NOR(C, C), NOR(D, D))))))))))767 compuertas · equivalencia verificada en todas las filas
La misma regla como código
Python
# -*- coding: utf-8 -*-
# Generated by Tangibool (tangibool.python/1). Do not edit by hand; regenerate from the source revision.
# Model: not stated
# Source revision: reference
# Interpretation status: not stated
"""Tangibool evaluator (decision model).
Generated deterministically from the validated Boolean model; it evaluates exactly that
model. It does not establish that the model is a complete, legal, or safe statement of a
real-world rule, and evaluating examples does not verify the rule.
Source revision: reference
Interpretation status: not stated
Exporter: 1.0.0 (format tangibool.python/1; engine 1.0.0; semantics tangibool-semantics/1)
Logic digest: 7287ed3ccdb2fd5ba20685cb8b39d7cd3986b9cd52310cf43c5d6d25c3603692
Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78
Inputs (dict keys, declared order) and generated parameter names:
'A' -> input_A
'B' -> input_B
'C' -> input_C
'D' -> input_D
Outputs (declared order) and their functions:
'f' -> output_f(inputs)
Assumptions (the declared scope, checked by in_scope(inputs)):
none; every complete assignment is in scope.
Input contract:
Every required input must be exactly True or False (type(value) is bool). Missing
inputs, None, strings, integers (including 0 and 1), and keys that are not declared
inputs raise InputError before anything is evaluated, including inputs that a
short-circuiting operator would never read. Results are always bool.
Scope:
Decision functions raise OutOfScopeError when the inputs violate an assumption; an
out-of-scope assignment is never turned into a False result. Pass check_scope=False
to evaluate without the scope check, and use in_scope(inputs) to test it separately.
Usage:
import tangibool_model as model
model.evaluate({'A': False, 'B': False, 'C': False, 'D': False})
# -> {'f': True}
model.output_f({'A': False, 'B': False, 'C': False, 'D': False})
# -> True
model.evaluate({'A': 1, 'B': False, 'C': False, 'D': False})
# raises InputError: 1 is an int, not a bool
"""
import collections.abc as _abc
from typing import Dict, Mapping, Tuple
__all__ = [
"MODEL_INFO",
"IDENTIFIER_MAP",
"INPUT_NAMES",
"OUTPUT_NAMES",
"ASSUMPTIONS",
"InputError",
"OutOfScopeError",
"minterm_index",
"in_scope",
"evaluate",
"output_f",
]
MODEL_INFO = {
"format": "tangibool.python/1",
"mode": "decision",
"model": None,
"revision": "reference",
"interpretation": None,
"exporter": "1.0.0",
"engine_version": "1.0.0",
"semantics_version": "tangibool-semantics/1",
"logic_digest": "7287ed3ccdb2fd5ba20685cb8b39d7cd3986b9cd52310cf43c5d6d25c3603692",
"assumptions_digest": "d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78",
"primary_output": "f",
"unused_inputs": (),
"subcircuits": (),
}
# Stable ID -> generated identifier (reversible mapping; names are exact, escaped strings).
IDENTIFIER_MAP = {
"v_79bf4b181173": {"kind": "input", "name": "A", "identifier": "input_A"},
"v_343a91721816": {"kind": "input", "name": "B", "identifier": "input_B"},
"v_bc9f47e4ba07": {"kind": "input", "name": "C", "identifier": "input_C"},
"v_649ea87deef0": {"kind": "input", "name": "D", "identifier": "input_D"},
"f_b1c238471ad8": {"kind": "output", "name": "f", "identifier": "output_f"},
}
INPUT_NAMES = ("A", "B", "C", "D")
OUTPUT_NAMES = ("f",)
ASSUMPTIONS = ()
_DECLARED_INPUTS = frozenset(INPUT_NAMES)
_SCOPE_INPUTS = ()
_ASSUMPTION_FORMULAS = {entry["name"]: entry["formula"] for entry in ASSUMPTIONS}
class InputError(ValueError):
"""Raised when inputs are missing, undeclared, or not exactly True/False.
Every required input must satisfy type(value) is bool. Missing inputs, None, strings,
integers (including 0 and 1), and keys that are not declared inputs are rejected before
anything is evaluated. A missing input is never treated as False. The individual problems
are listed in the problems attribute.
"""
def __init__(self, problems):
self.problems = tuple(problems)
super().__init__("Invalid inputs: " + "; ".join(self.problems))
class OutOfScopeError(ValueError):
"""Raised when the inputs violate the model's assumptions (its declared scope).
Outside its assumptions the rule has no decision: this error is never a False result.
The names of the violated assumptions are in the violated attribute.
"""
def __init__(self, violated):
self.violated = tuple(violated)
details = ", ".join(name + " (" + _ASSUMPTION_FORMULAS.get(name, "?") + ")" for name in self.violated)
super().__init__(
"Out of scope: the inputs violate "
+ ("assumption " if len(self.violated) == 1 else "assumptions ")
+ details
+ ". The rule has no decision outside its assumptions; this is not a False result."
)
def _short_repr(value: object) -> str:
text = repr(value)
return text if len(text) <= 60 else text[:57] + "..."
def _checked_inputs(inputs: Mapping[str, bool], required: Tuple[str, ...], check_scope: bool) -> Dict[str, bool]:
"""Validate inputs strictly before anything is evaluated and return a plain copy."""
if type(check_scope) is not bool:
raise TypeError("check_scope must be True or False")
if not isinstance(inputs, _abc.Mapping):
raise InputError(["inputs must be a mapping from input names to True/False, got " + type(inputs).__name__])
problems = []
for key in inputs:
if type(key) is not str or key not in _DECLARED_INPUTS:
declared = ", ".join(repr(name) for name in INPUT_NAMES) or "none"
problems.append("undeclared input " + _short_repr(key) + " (declared inputs: " + declared + ")")
needed = tuple(required) + (_SCOPE_INPUTS if check_scope else ())
for name in needed:
if name not in inputs:
problems.append("missing required input " + repr(name))
for key, value in inputs.items():
if type(key) is str and key in _DECLARED_INPUTS and type(value) is not bool:
problems.append(
"input " + repr(key) + " must be True or False (type bool), got "
+ type(value).__name__ + " " + _short_repr(value)
)
if problems:
raise InputError(list(dict.fromkeys(problems)))
return dict(inputs.items())
def _require_bool_args(function: str, pairs: Tuple[Tuple[str, object], ...]) -> None:
problems = [
"argument " + repr(name) + " of " + function + " must be True or False (type bool), got "
+ type(value).__name__ + " " + _short_repr(value)
for name, value in pairs
if type(value) is not bool
]
if problems:
raise InputError(problems)
def minterm_index(*values: bool) -> int:
"""Row index of an assignment over a declared variable order.
The first value is the most significant bit, so all-False is row 0. Used for indexed
minterm (sum) and maxterm (product) forms.
"""
index = 0
for value in values:
if type(value) is not bool:
raise InputError(["minterm_index() takes True/False values, got " + type(value).__name__ + " " + _short_repr(value)])
index = index * 2 + (1 if value else 0)
return index
def _scope_values(values: Dict[str, bool]) -> Tuple[Tuple[str, bool], ...]:
"""Value of every enabled, confirmed assumption for validated inputs, in declared order."""
return ()
def _require_in_scope(values: Dict[str, bool]) -> None:
violated = tuple(name for name, holds in _scope_values(values) if not holds)
if violated:
raise OutOfScopeError(violated)
def in_scope(inputs: Mapping[str, bool]) -> bool:
"""True when the inputs satisfy every assumption (the model's declared scope).
Requires the inputs the assumptions read; raises InputError for invalid inputs.
"""
values = _checked_inputs(inputs, (), True)
return all(holds for _, holds in _scope_values(values))
# ---- Formula bodies (inputs are validated by the public functions below) ----
def _compute_output_f(input_A: bool, input_B: bool, input_C: bool, input_D: bool) -> bool:
"""Decision output 'f': \u03a3m(A, B, C, D; 0, 2, 5, 7, 8, 10, 13, 15)"""
return minterm_index(input_A, input_B, input_C, input_D) in (0, 2, 5, 7, 8, 10, 13, 15)
# ---- Public API ----
def output_f(inputs: Mapping[str, bool], *, check_scope: bool = True) -> bool:
"""Decision output 'f' (stable ID f_b1c238471ad8).
'f' := \u03a3m(A, B, C, D; 0, 2, 5, 7, 8, 10, 13, 15)
Required inputs: 'A', 'B', 'C', 'D'.
Raises InputError for missing, undeclared, or non-bool inputs, and OutOfScopeError
when check_scope is True and the inputs violate an assumption.
"""
values = _checked_inputs(inputs, ("A", "B", "C", "D"), check_scope)
if check_scope:
_require_in_scope(values)
output_f_value = _compute_output_f(values["A"], values["B"], values["C"], values["D"])
return output_f_value
def evaluate(inputs: Mapping[str, bool], *, check_scope: bool = True) -> Dict[str, bool]:
"""Evaluate every output (declared order); each output is computed once.
Required inputs: 'A', 'B', 'C', 'D'.
Raises InputError for missing, undeclared, or non-bool inputs, and OutOfScopeError
when check_scope is True and the inputs violate an assumption.
"""
values = _checked_inputs(inputs, ("A", "B", "C", "D"), check_scope)
if check_scope:
_require_in_scope(values)
output_f_value = _compute_output_f(values["A"], values["B"], values["C"], values["D"])
return {
"f": output_f_value,
}
PostgreSQL
-- Tangibool PostgreSQL export (tangibool.postgresql/1)
-- Target: PostgreSQL 16 or later with typed boolean inputs; tested with PostgreSQL 18.3 (PGlite 0.5.8).
-- Not a claim of compatibility with other SQL dialects.
-- Model: not stated
-- Source revision: reference
-- Interpretation status: not stated
-- Exporter: 1.0.0 (engine 1.0.0; semantics tangibool-semantics/1)
-- Logic digest: 7287ed3ccdb2fd5ba20685cb8b39d7cd3986b9cd52310cf43c5d6d25c3603692
-- Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78
-- Mode: decision
--
-- Read-only: this file contains only WITH / VALUES / SELECT statements. No DDL, DML,
-- procedures, credentials, network access, or database changes. The expressions are pure
-- Boolean expressions, so their result does not depend on SQL evaluation order.
--
-- NON-NULL INPUT PRECONDITION: NULL is not a truth value of this rule. Every fragment below
-- is defined only when every input column it reads is a non-NULL boolean. The guard template
-- (section 2) marks any NULL input as 'invalid_input' and any row that violates the
-- assumptions as 'out_of_scope', and fills output columns only for 'ok' rows; a NULL in an
-- output column of another row is an envelope marker, not a third truth value. Never wrap
-- the fragments in COALESCE(..., FALSE) or otherwise choose a meaning for unknown inputs.
-- This evaluates the supplied model; it does not show that the model is a complete, legal,
-- or safe statement of a real-world rule.
--
-- Input columns (stable ID: name -> column):
-- v_79bf4b181173: A -> "in_A"
-- v_343a91721816: B -> "in_B"
-- v_bc9f47e4ba07: C -> "in_C"
-- v_649ea87deef0: D -> "in_D"
-- Output columns:
-- f_b1c238471ad8: f -> "out_f"
-- Assumptions (scope K; exported separately and never folded into an output):
-- none; every complete input row is in scope.
-- ----------------------------------------------------------------------------------------------
-- 1. Expression fragments (parenthesised; non-NULL boolean inputs required)
-- ----------------------------------------------------------------------------------------------
--
-- [out_f] output f (stable ID f_b1c238471ad8)
-- f := \u03a3m(A, B, C, D; 0, 2, 5, 7, 8, 10, 13, 15)
-- PRECONDITION: "in_A", "in_B", "in_C", "in_D" are non-NULL booleans.
-- (((NOT "in_A") AND (NOT "in_B") AND (NOT "in_C") AND (NOT "in_D")) OR ((NOT "in_A") AND (NOT "in_B") AND "in_C" AND (NOT "in_D")) OR ((NOT "in_A") AND "in_B" AND (NOT "in_C") AND "in_D") OR ((NOT "in_A") AND "in_B" AND "in_C" AND "in_D") OR ("in_A" AND (NOT "in_B") AND (NOT "in_C") AND (NOT "in_D")) OR ("in_A" AND (NOT "in_B") AND "in_C" AND (NOT "in_D")) OR ("in_A" AND "in_B" AND (NOT "in_C") AND "in_D") OR ("in_A" AND "in_B" AND "in_C" AND "in_D"))
--
-- ----------------------------------------------------------------------------------------------
-- 2. Guard template (read-only SELECT over an inputs list)
-- ----------------------------------------------------------------------------------------------
-- Replace the example rows between the markers with your own rows, or replace the inputs
-- CTE with a SELECT that provides the boolean columns listed in the header. status is
-- 'invalid_input' when any input is NULL, 'out_of_scope' when the assumptions are false, and
-- 'ok' otherwise; output columns are filled only for 'ok' rows (NULL elsewhere is an
-- envelope marker). Assumption columns are shown for rows with complete inputs.
WITH inputs ("row_id", "in_A", "in_B", "in_C", "in_D") AS (
-- tangibool:example-rows:begin
VALUES
(1, FALSE, FALSE, FALSE, FALSE),
(2, FALSE, FALSE, FALSE, TRUE),
(3, FALSE, FALSE, TRUE, FALSE),
(4, FALSE, FALSE, TRUE, TRUE),
(5, FALSE, TRUE, FALSE, FALSE),
(6, FALSE, TRUE, FALSE, TRUE),
(7, FALSE, TRUE, TRUE, FALSE),
(8, FALSE, TRUE, TRUE, TRUE),
(9, TRUE, FALSE, FALSE, FALSE),
(10, TRUE, FALSE, FALSE, TRUE),
(11, TRUE, FALSE, TRUE, FALSE),
(12, TRUE, FALSE, TRUE, TRUE),
(13, TRUE, TRUE, FALSE, FALSE),
(14, TRUE, TRUE, FALSE, TRUE),
(15, TRUE, TRUE, TRUE, FALSE),
(16, TRUE, TRUE, TRUE, TRUE),
(17, NULL::boolean, FALSE, FALSE, FALSE)
-- tangibool:example-rows:end
),
checked AS (
SELECT
inputs.*,
CASE
WHEN "in_A" IS NULL OR "in_B" IS NULL OR "in_C" IS NULL OR "in_D" IS NULL THEN 'invalid_input'
ELSE 'ok'
END AS "status"
FROM inputs
)
SELECT
"row_id",
"in_A",
"in_B",
"in_C",
"in_D",
"status",
CASE WHEN "status" = 'ok' THEN (((NOT "in_A") AND (NOT "in_B") AND (NOT "in_C") AND (NOT "in_D")) OR ((NOT "in_A") AND (NOT "in_B") AND "in_C" AND (NOT "in_D")) OR ((NOT "in_A") AND "in_B" AND (NOT "in_C") AND "in_D") OR ((NOT "in_A") AND "in_B" AND "in_C" AND "in_D") OR ("in_A" AND (NOT "in_B") AND (NOT "in_C") AND (NOT "in_D")) OR ("in_A" AND (NOT "in_B") AND "in_C" AND (NOT "in_D")) OR ("in_A" AND "in_B" AND (NOT "in_C") AND "in_D") OR ("in_A" AND "in_B" AND "in_C" AND "in_D")) END AS "out_f"
FROM checked
ORDER BY "row_id";
SMT-LIB
; Tangibool SMT-LIB export (tangibool.smtlib/1) ; Profile: SMT-LIB 2.6 Boolean subset (QF_UF): Bool constants, define-fun, let, push/pop, assert, check-sat, echo. ; Tested with Z3 5.1.0 (z3-solver 5.2.0, WebAssembly build). ; Model: not stated ; Source revision: reference ; Interpretation status: not stated ; Exporter: 1.0.0 (engine 1.0.0; semantics tangibool-semantics/1) ; Logic digest: 7287ed3ccdb2fd5ba20685cb8b39d7cd3986b9cd52310cf43c5d6d25c3603692 ; Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78 ; Mode: decision ; ; Reading results: each query block states what sat and unsat mean for its question. A sat ; answer comes with a witness or counterexample (ask for it with (get-model) after sat only); ; unsat settles that scoped query and is solver-checked, not an independently checked proof ; certificate; unknown settles nothing. Blocks are scoped with push/pop, so assertions never ; accumulate across questions. This checks the supplied model, not whether it is a complete, ; legal, or safe statement of a real-world rule. ; ; Symbols (stable ID: name -> symbol): ; v_79bf4b181173: A -> in_A ; v_343a91721816: B -> in_B ; v_bc9f47e4ba07: C -> in_C ; v_649ea87deef0: D -> in_D ; f_b1c238471ad8: f -> out_f (set-option :produce-models true) (set-info :smt-lib-version 2.6) (set-logic QF_UF) ; ---- Inputs (declared order) (declare-const in_A Bool) ; A (declare-const in_B Bool) ; B (declare-const in_C Bool) ; C (declare-const in_D Bool) ; D ; ---- Outputs (dependencies first) ; output f (stable ID f_b1c238471ad8): \u03a3m(A, B, C, D; 0, 2, 5, 7, 8, 10, 13, 15) (define-fun out_f () Bool (or (and (not in_A) (not in_B) (not in_C) (not in_D)) (and (not in_A) (not in_B) in_C (not in_D)) (and (not in_A) in_B (not in_C) in_D) (and (not in_A) in_B in_C in_D) (and in_A (not in_B) (not in_C) (not in_D)) (and in_A (not in_B) in_C (not in_D)) (and in_A in_B (not in_C) in_D) (and in_A in_B in_C in_D))) ; ---- Assumptions (the scope K; never folded into an output) ; K: conjunction of the enabled, confirmed assumptions (true when there are none) (define-fun K () Bool true) ; ---- Definitions only: nothing is asserted and no check is run. ; Add (assert ...) and (check-sat) inside (push 1) ... (pop 1) to ask a question.
LaTeX
f = \sum m_{(A, B, C, D)}(0, 2, 5, 7, 8, 10, 13, 15)Preguntas
¿Por qué el solucionador se detiene en 4 variables cuando otros sitios ofrecen de 5 a 8?
Un mapa de 5 o más variables son dos o más mapas de 4 variables apilados, y las reglas de adyacencia dejan de ser visuales. Las herramientas que aceptan más variables usan por debajo el método tabular. El límite del motor se declara en lugar de ocultarse; para funciones mayores, el conversor a FNC y FND usa implicantes primos.
¿Puedo elegir mis propias agrupaciones?
En la app, sí: haz clic en las celdas para seleccionar rectángulos, añade grupos, y el motor valida cada grupo (tamaño, forma, continuidad por los bordes) y deriva la expresión de tu cobertura. Esta página muestra la cobertura sugerida por el motor.
¿Da también el producto de sumas?
La herramienta de mapas deriva la suma de productos a partir de las celdas con 1. El conversor a FNC da el producto de sumas, y la página de comparativa muestra los dos para la misma función.
Relacionado
Herramientas
- Generador de tablas de verdad: cualquier expresión booleana, hasta 12 variables, con columnas intermedias
- Calculadora y simplificador de álgebra de Boole paso a paso (cada ley nombrada y verificada)
- Conversor a FNC y FND: formas normales conjuntiva y disyuntiva, mintérminos y maxtérminos
- Conversor a solo NAND o solo NOR con demostración de equivalencia
- Comprobador de equivalencia lógica: dos expresiones, veredicto exacto, contraejemplo
- Comprobador de validez de argumentos: premisas, conclusión, contraejemplo o demostración
- Generador de circuitos lógicos: de expresión booleana a diagrama de compuertas (SVG)
- De expresión booleana a Python, SQL, SMT-LIB y LaTeX
Ejercicios
- Ejercicios de mapas de Karnaugh, 2 variables
- Ejercicios de mapas de Karnaugh, 3 variables
- Ejercicios de mapas de Karnaugh, 4 variables
Herramientas
- Generador de tablas de verdad: cualquier expresión booleana, hasta 12 variables, con columnas intermedias
- Calculadora y simplificador de álgebra de Boole paso a paso (cada ley nombrada y verificada)
- Conversor a FNC y FND: formas normales conjuntiva y disyuntiva, mintérminos y maxtérminos
- Conversor a solo NAND o solo NOR con demostración de equivalencia
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.