Política de contraseñas: longitud_ok AND (tiene_digito OR tiene_simbolo) AND NOT comun
Una política de contraseñas, length_ok AND (has_digit OR has_symbol) AND NOT common: dieciséis filas con tres que aceptan, una FND de dos términos, dos grupos de Karnaugh, y una forma NOR de 8 compuertas frente a 23 NAND.
Una contraseña se acepta cuando es suficientemente larga, contiene un dígito o un símbolo, y no está en la lista de contraseñas comunes. La lectura del motor enumera los tres requisitos: length_ok verdadero, al menos uno entre has_digit y has_symbol, common falso. En la tabla de dieciséis filas la salida es verdadera en tres filas, Σm(10, 12, 14): larga con símbolo, larga con dígito, o larga con ambos, ninguna de ellas común.
Las comprobaciones: no es tautología, contraejemplo las cuatro entradas en FALSO; satisfacible, testigo length_ok = VERDADERO, has_digit = FALSO, has_symbol = VERDADERO, common = FALSO. El simplificador no encontró ninguna ley que acorte la regla de cuatro operadores; el conversor a FNC la devuelve sin cambios, tres cláusulas con cuatro literales. El conversor a FND aplica dos distributividades y da (length_ok AND has_digit AND NOT common) OR (length_ok AND has_symbol AND NOT common), dos términos y seis literales, los mismos dos grupos que dibuja el mapa de Karnaugh en las celdas 12 y 14 y en las celdas 10 y 14, dos implicantes primos. Compuertas: 23 NAND, 8 NOR.
Los validadores de contraseñas son una fuente clásica de comportamiento incoherente entre cliente y servidor, porque la regla se reimplementa en dos lenguajes. Lo que hay que vigilar es el OR del medio: un dígito o un símbolo, no ambos, y las tres filas verdaderas de la tabla incluyen la fila con solo símbolo y la fila con solo dígito. Un validador que exija los dos rechaza dos de las tres filas que aceptan. La tabla, o su exportación a CSV, es un juego de pruebas neutral respecto al lenguaje para las dos implementaciones.
accepted := length_ok AND (has_digit OR has_symbol) AND NOT common · salida
Comprobaciones exactas
Tabla de verdad (16 filas)
| # | length_ok | has_digit | has_symbol | common | accepted |
|---|---|---|---|---|---|
| 0 | FALSO | FALSO | FALSO | FALSO | FALSO |
| 1 | FALSO | FALSO | FALSO | VERDADERO | FALSO |
| 2 | FALSO | FALSO | VERDADERO | FALSO | FALSO |
| 3 | FALSO | FALSO | VERDADERO | VERDADERO | FALSO |
| 4 | FALSO | VERDADERO | FALSO | FALSO | FALSO |
| 5 | FALSO | VERDADERO | FALSO | VERDADERO | FALSO |
| 6 | FALSO | VERDADERO | VERDADERO | FALSO | FALSO |
| 7 | FALSO | VERDADERO | VERDADERO | VERDADERO | FALSO |
| 8 | VERDADERO | FALSO | FALSO | FALSO | FALSO |
| 9 | VERDADERO | FALSO | FALSO | VERDADERO | FALSO |
| 10 | VERDADERO | FALSO | VERDADERO | FALSO | VERDADERO |
| 11 | VERDADERO | FALSO | VERDADERO | VERDADERO | FALSO |
| 12 | VERDADERO | VERDADERO | FALSO | FALSO | VERDADERO |
| 13 | VERDADERO | VERDADERO | FALSO | VERDADERO | FALSO |
| 14 | VERDADERO | VERDADERO | VERDADERO | FALSO | VERDADERO |
| 15 | VERDADERO | VERDADERO | VERDADERO | VERDADERO | FALSO |
Lectura en lenguaje claro
Principianteaccepted es verdadero exactamente cuando se cumplen todas las condiciones siguientes:
1. length_ok es verdadero
2. al menos uno entre has_digit y has_symbol es verdadero (pueden serlo ambos)
3. common es falso
En todos los demás casos, accepted es falso.
Sobre los operadores:
- AND (Y) solo es verdadero cuando todas sus partes son verdaderas.
- OR (O) es inclusivo: es verdadero en cuanto al menos una parte es verdadera, también cuando lo son varias.
- NOT (NO) invierte un valor: lo verdadero pasa a ser falso y lo falso, verdadero.
Intermedioaccepted es verdadero exactamente cuando se cumplen todas las condiciones siguientes:
1. length_ok es verdadero
2. al menos uno entre has_digit y has_symbol es verdadero (pueden serlo ambos)
3. common es falso
En todos los demás casos, accepted es falso.
Avanzadoaccepted es verdadero exactamente cuando se cumplen todas las condiciones siguientes [conjunción ∧]:
1. length_ok es verdadero
2. al menos uno entre has_digit y has_symbol es verdadero (pueden serlo ambos) [disyunción inclusiva ∨]
3. common es falso [negación ¬]
En todos los demás casos, accepted es falso.
Notación formal: length_ok ∧ (has_digit ∨ has_symbol) ∧ ¬common
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.
length_ok AND (has_digit OR has_symbol) AND NOT common
Mapa de Karnaugh
- celdas m12, m14
length_ok AND has_digit AND NOT common - celdas m10, m14
length_ok AND has_symbol AND NOT common
Mintérminos y maxtérminos
accepted(length_ok, has_digit, has_symbol, common) = Σm(10, 12, 14)accepted(length_ok, has_digit, has_symbol, common) = ΠM(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15)Orden de variables: length_ok, has_digit, has_symbol, common · 16 filas
Formas normales
Forma normal conjuntiva (FNC)
length_ok AND (has_digit OR has_symbol) AND NOT common3 cláusulas, 4 literales · complete
Forma normal disyuntiva (FND)
(length_ok AND has_digit AND NOT common) OR (length_ok AND has_symbol AND NOT common)2 términos, 6 literales · complete · Distributividad ×2
Solo NAND, solo NOR
Forma solo con NAND
NAND(NAND(NAND(NAND(length_ok, NAND(NAND(has_digit, has_digit), NAND(has_symbol, has_symbol))), NAND(length_ok, NAND(NAND(has_digit, has_digit), NAND(has_symbol, has_symbol)))), NAND(common, common)), NAND(NAND(NAND(length_ok, NAND(NAND(has_digit, has_digit), NAND(has_symbol, has_symbol))), NAND(length_ok, NAND(NAND(has_digit, has_digit), NAND(has_symbol, has_symbol)))), NAND(common, common)))23 compuertas · equivalencia verificada en todas las filas
Forma solo con NOR
NOR(NOR(NOR(NOR(length_ok, length_ok), NOR(has_digit, has_symbol)), NOR(NOR(length_ok, length_ok), NOR(has_digit, has_symbol))), common)8 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: 4e41d480db12655d9c91963d520ecd09c530586ef901c5da7d17c0b9d23a937c
Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78
Inputs (dict keys, declared order) and generated parameter names:
'length_ok' -> input_length_ok
'has_digit' -> input_has_digit
'has_symbol' -> input_has_symbol
'common' -> input_common
Outputs (declared order) and their functions:
'accepted' -> output_accepted(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({'length_ok': False, 'has_digit': False, 'has_symbol': False, 'common': False})
# -> {'accepted': False}
model.output_accepted({'length_ok': False, 'has_digit': False, 'has_symbol': False, 'common': False})
# -> False
model.evaluate({'length_ok': 1, 'has_digit': False, 'has_symbol': False, 'common': 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_accepted",
]
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": "4e41d480db12655d9c91963d520ecd09c530586ef901c5da7d17c0b9d23a937c",
"assumptions_digest": "d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78",
"primary_output": "accepted",
"unused_inputs": (),
"subcircuits": (),
}
# Stable ID -> generated identifier (reversible mapping; names are exact, escaped strings).
IDENTIFIER_MAP = {
"v_8e59f235b584": {"kind": "input", "name": "length_ok", "identifier": "input_length_ok"},
"v_6555d4fcf55e": {"kind": "input", "name": "has_digit", "identifier": "input_has_digit"},
"v_d6dca9d2de39": {"kind": "input", "name": "has_symbol", "identifier": "input_has_symbol"},
"v_4a0105a57b99": {"kind": "input", "name": "common", "identifier": "input_common"},
"f_c8d95c9b38ed": {"kind": "output", "name": "accepted", "identifier": "output_accepted"},
}
INPUT_NAMES = ("length_ok", "has_digit", "has_symbol", "common")
OUTPUT_NAMES = ("accepted",)
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_accepted(input_length_ok: bool, input_has_digit: bool, input_has_symbol: bool, input_common: bool) -> bool:
"""Decision output 'accepted': length_ok AND (has_digit OR has_symbol) AND NOT common"""
return input_length_ok and (input_has_digit or input_has_symbol) and (not input_common)
# ---- Public API ----
def output_accepted(inputs: Mapping[str, bool], *, check_scope: bool = True) -> bool:
"""Decision output 'accepted' (stable ID f_c8d95c9b38ed).
'accepted' := length_ok AND (has_digit OR has_symbol) AND NOT common
Required inputs: 'length_ok', 'has_digit', 'has_symbol', 'common'.
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, ("length_ok", "has_digit", "has_symbol", "common"), check_scope)
if check_scope:
_require_in_scope(values)
output_accepted_value = _compute_output_accepted(values["length_ok"], values["has_digit"], values["has_symbol"], values["common"])
return output_accepted_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: 'length_ok', 'has_digit', 'has_symbol', 'common'.
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, ("length_ok", "has_digit", "has_symbol", "common"), check_scope)
if check_scope:
_require_in_scope(values)
output_accepted_value = _compute_output_accepted(values["length_ok"], values["has_digit"], values["has_symbol"], values["common"])
return {
"accepted": output_accepted_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: 4e41d480db12655d9c91963d520ecd09c530586ef901c5da7d17c0b9d23a937c
-- 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_8e59f235b584: length_ok -> "in_length_ok"
-- v_6555d4fcf55e: has_digit -> "in_has_digit"
-- v_d6dca9d2de39: has_symbol -> "in_has_symbol"
-- v_4a0105a57b99: common -> "in_common"
-- Output columns:
-- f_c8d95c9b38ed: accepted -> "out_accepted"
-- 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_accepted] output accepted (stable ID f_c8d95c9b38ed)
-- accepted := length_ok AND (has_digit OR has_symbol) AND NOT common
-- PRECONDITION: "in_length_ok", "in_has_digit", "in_has_symbol", "in_common" are non-NULL booleans.
-- ("in_length_ok" AND ("in_has_digit" OR "in_has_symbol") AND (NOT "in_common"))
--
-- ----------------------------------------------------------------------------------------------
-- 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_length_ok", "in_has_digit", "in_has_symbol", "in_common") 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_length_ok" IS NULL OR "in_has_digit" IS NULL OR "in_has_symbol" IS NULL OR "in_common" IS NULL THEN 'invalid_input'
ELSE 'ok'
END AS "status"
FROM inputs
)
SELECT
"row_id",
"in_length_ok",
"in_has_digit",
"in_has_symbol",
"in_common",
"status",
CASE WHEN "status" = 'ok' THEN ("in_length_ok" AND ("in_has_digit" OR "in_has_symbol") AND (NOT "in_common")) END AS "out_accepted"
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: 4e41d480db12655d9c91963d520ecd09c530586ef901c5da7d17c0b9d23a937c ; 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_8e59f235b584: length_ok -> in_length_ok ; v_6555d4fcf55e: has_digit -> in_has_digit ; v_d6dca9d2de39: has_symbol -> in_has_symbol ; v_4a0105a57b99: common -> in_common ; f_c8d95c9b38ed: accepted -> out_accepted (set-option :produce-models true) (set-info :smt-lib-version 2.6) (set-logic QF_UF) ; ---- Inputs (declared order) (declare-const in_length_ok Bool) ; length_ok (declare-const in_has_digit Bool) ; has_digit (declare-const in_has_symbol Bool) ; has_symbol (declare-const in_common Bool) ; common ; ---- Outputs (dependencies first) ; output accepted (stable ID f_c8d95c9b38ed): length_ok AND (has_digit OR has_symbol) AND NOT common (define-fun out_accepted () Bool (and in_length_ok (or in_has_digit in_has_symbol) (not in_common))) ; ---- 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
accepted = \mathit{length\_ok} \cdot \left(\mathit{has\_digit} + \mathit{has\_symbol}\right) \cdot \overline{\mathit{common}}El error habitual
Exigir dígito y símbolo a la vez, has_digit AND has_symbol, cuando la política dice uno u otro. La regla prevista acepta tres filas; la versión más estricta acepta una, length_ok = VERDADERO, has_digit = VERDADERO, has_symbol = VERDADERO, common = FALSO. Quien tenga una contraseña larga con un dígito es rechazado sin ninguna razón declarada.
Preguntas
¿Por qué los tres mintérminos son números pares?
common es el bit menos significativo y debe ser FALSO para aceptar, así que toda fila que acepta es par. length_ok, el bit más significativo, aporta 8, y los bits de dígito o símbolo suman 4 o 2 o ambos, dando 12, 10 y 14.
Relacionado
Operadores y compuertas
- Compuerta NOT (inversor): tabla de verdad, símbolo y el operador NOT
- Compuerta AND (puerta Y): tabla de verdad de 2, 3 y 4 entradas, símbolo y expresión
- Compuerta OR (puerta O): tabla de verdad de 2, 3 y 4 entradas
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)
- Solucionador de mapas de Karnaugh: de 2 a 4 variables, agrupaciones, SOP y POS
Véase también
- Elegibilidad de un préstamo: ingresos_ok AND (credito_ok OR avalista) AND NOT quiebra
- Regla de envío gratis: (mas_de_50 OR prime) AND NOT voluminoso AND nacional
- Derivar casos de prueba de una tabla de verdad sin probar todas las filas
- Escribir reglas de negocio en lenguaje claro que se traduzcan a lógica
- De expresión booleana a Python, SQL, SMT-LIB y LaTeX
- Operadores lógicos en JavaScript: &&, ||, !, truthiness y precedencia
Ejemplos resueltos
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