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化簡 $$$\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B}$$$
相關計算器: 真值表計算器
您的輸入
化簡布林運算式 $$$\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B}$$$。
解答
應用交換律：
$${\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B}\right)} = {\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A\right)}$$以 $$$x = \overline{B}$$$ 套用冪等律 $$$x \cdot x = x$$$：
$$\overline{A} \cdot {\color{red}\left(\overline{B} \cdot \overline{B}\right)} \cdot \overline{C} \cdot \overline{D} \cdot A = \overline{A} \cdot {\color{red}\left(\overline{B}\right)} \cdot \overline{C} \cdot \overline{D} \cdot A$$應用交換律：
$${\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A\right)} = {\color{red}\left(A \cdot \overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}\right)}$$將補集法則 $$$x \cdot \overline{x} = 0$$$ 應用於 $$$x = A$$$：
$${\color{red}\left(A \cdot \overline{A}\right)} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}$$應用交換律：
$${\color{red}\left(0 \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}\right)} = {\color{red}\left(\overline{B} \cdot 0 \cdot \overline{C} \cdot \overline{D}\right)}$$對 $$$x = \overline{B}$$$ 應用支配（零、歸零）律 $$$x \cdot 0 = 0$$$：
$${\color{red}\left(\overline{B} \cdot 0\right)} \cdot \overline{C} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{C} \cdot \overline{D}$$應用交換律：
$${\color{red}\left(0 \cdot \overline{C} \cdot \overline{D}\right)} = {\color{red}\left(\overline{C} \cdot 0 \cdot \overline{D}\right)}$$對 $$$x = \overline{C}$$$ 應用支配（零、歸零）律 $$$x \cdot 0 = 0$$$：
$${\color{red}\left(\overline{C} \cdot 0\right)} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{D}$$應用交換律：
$${\color{red}\left(0 \cdot \overline{D}\right)} = {\color{red}\left(\overline{D} \cdot 0\right)}$$對 $$$x = \overline{D}$$$ 應用支配（零、歸零）律 $$$x \cdot 0 = 0$$$：
$${\color{red}\left(\overline{D} \cdot 0\right)} = {\color{red}\left(0\right)}$$答案
$$$\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B} = 0$$$
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