# 组合逻辑电路

## 组合电路的设计

### 表示

A B C 输出 逻辑等价
F F F F ${\displaystyle \neg A\wedge \neg B\wedge \neg C}$
F F T F ${\displaystyle \neg A\wedge \neg B\wedge C}$
F T F F ${\displaystyle \neg A\wedge B\wedge \neg C}$
F T T F ${\displaystyle \neg A\wedge B\wedge C}$
T F F T ${\displaystyle A\wedge \neg B\wedge \neg C}$
T F T F ${\displaystyle A\wedge \neg B\wedge C}$
T T F F ${\displaystyle A\wedge B\wedge \neg C}$
T T T T ${\displaystyle A\wedge B\wedge C}$

${\displaystyle (A\wedge \neg B\wedge \neg C)\vee (A\wedge B\wedge C)\,}$

${\displaystyle A\wedge ((\neg B\wedge \neg C)\vee (B\wedge C))\,}$

### 逻辑公式最小化

{\displaystyle {\begin{aligned}(A\vee B)\wedge (A\vee C)&=A\vee (B\wedge C)\\(A\wedge B)\vee (A\wedge C)&=A\wedge (B\vee C)\end{aligned}}}
{\displaystyle {\begin{aligned}A\vee (A\wedge B)&=A\\A\wedge (A\vee B)&=A\end{aligned}}}
{\displaystyle {\begin{aligned}A\vee (\lnot A\wedge B)&=A\vee B\\A\wedge (\lnot A\vee B)&=A\wedge B\end{aligned}}}
{\displaystyle {\begin{aligned}(A\vee B)\wedge (\lnot A\vee B)&=B\\(A\wedge B)\vee (\lnot A\wedge B)&=B\end{aligned}}}
{\displaystyle {\begin{aligned}(A\wedge B)\vee (\lnot A\wedge C)\vee (B\wedge C)&=(A\wedge B)\vee (\lnot A\wedge C)\\(A\vee B)\wedge (\lnot A\vee C)\wedge (B\vee C)&=(A\vee B)\wedge (\lnot A\vee C)\end{aligned}}}

1. ^ Lewin, Douglas. Logical Design of Switching Circuits 2nd. Thomas Nelson and Sons. 1974: 162–3. ISBN 017-771044-6.