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Simplifique $$$\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B}$$$
Calculadora relacionada: Calculadora de Tabela-Verdade
Sua entrada
Simplifique a expressão booleana $$$\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B}.$$$
Solução
Aplique a lei comutativa:
$${\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B}\right)} = {\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A\right)}$$Aplique a lei idempotente $$$x \cdot x = x$$$ com $$$x = \overline{B}$$$:
$$\overline{A} \cdot {\color{red}\left(\overline{B} \cdot \overline{B}\right)} \cdot \overline{C} \cdot \overline{D} \cdot A = \overline{A} \cdot {\color{red}\left(\overline{B}\right)} \cdot \overline{C} \cdot \overline{D} \cdot A$$Aplique a lei comutativa:
$${\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A\right)} = {\color{red}\left(A \cdot \overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}\right)}$$Aplique a lei do complemento $$$x \cdot \overline{x} = 0$$$ com $$$x = A$$$:
$${\color{red}\left(A \cdot \overline{A}\right)} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}$$Aplique a lei comutativa:
$${\color{red}\left(0 \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}\right)} = {\color{red}\left(\overline{B} \cdot 0 \cdot \overline{C} \cdot \overline{D}\right)}$$Aplique a lei dominante (do nulo, do anulamento) $$$x \cdot 0 = 0$$$ com $$$x = \overline{B}$$$:
$${\color{red}\left(\overline{B} \cdot 0\right)} \cdot \overline{C} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{C} \cdot \overline{D}$$Aplique a lei comutativa:
$${\color{red}\left(0 \cdot \overline{C} \cdot \overline{D}\right)} = {\color{red}\left(\overline{C} \cdot 0 \cdot \overline{D}\right)}$$Aplique a lei dominante (do nulo, do anulamento) $$$x \cdot 0 = 0$$$ com $$$x = \overline{C}$$$:
$${\color{red}\left(\overline{C} \cdot 0\right)} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{D}$$Aplique a lei comutativa:
$${\color{red}\left(0 \cdot \overline{D}\right)} = {\color{red}\left(\overline{D} \cdot 0\right)}$$Aplique a lei dominante (do nulo, do anulamento) $$$x \cdot 0 = 0$$$ com $$$x = \overline{D}$$$:
$${\color{red}\left(\overline{D} \cdot 0\right)} = {\color{red}\left(0\right)}$$Resposta
$$$\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B} = 0$$$