门 | GATE-CS-2006 | 第57章

简介

GATE-CS-2006 是印度全国研究生入学考试(GATE)中计算机科学工程(CS)的一道题目。该题目涉及到门、时序电路、组合电路等内容，是计算机工程师必须掌握的基础知识之一。

题目描述

题目链接：https://gateoverflow.in/634/gate2006-57

有一个5个输入端口A、B、C、D 和 E, 和一个输出端口F的门电路如下所示:

它的真值表可以表示为:

| A | B | C | D | E | F | | :---: | :---: | :---: | :---: | :---: | :---: | | 0 | 0 | 0 | 0 | 0 | 1 | | 0 | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 0 | 1 | 1 | 1 | | 0 | 0 | 1 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | 1 | 1 | | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 0 | 1 | | 0 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | 0 | 1 | | 0 | 1 | 0 | 1 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | 0 | | 0 | 1 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | 0 | | 1 | 0 | 0 | 0 | 1 | 1 | | 1 | 0 | 0 | 1 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | 0 | | 1 | 0 | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | 1 | 1 | | 1 | 0 | 1 | 1 | 0 | 1 | | 1 | 0 | 1 | 1 | 1 | 0 | | 1 | 1 | 0 | 0 | 0 | 0 | | 1 | 1 | 0 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | | 1 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | 0 | | 1 | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | 1 | 0 |

基于上述真值表，编写一种gate电路实现该电路的功能。

解析

为了解决这个问题，我们需要分析真值表并提取其规律，然后构建相应的门电路。

通过观察真值表，我们可以发现，只有在输入端口A或D至少一个为1并且B和C都为0时，输出端口F才为1。因此，我们可以使用 OR 门来连接 A 和 D 来获取这个条件。另外，我们可以利用 AND 门来判断 B 和 C 是否恒为 0。

为此，我们可以使用以下门电路：

接下来的代码展示了如何实现上述电路的功能：

```python
def gate_circuit(A, B, C, D, E):
    return (A or D) and (not B) and (not C)

现在我们可以使用上述代码来测试输入中的各个值，并验证电路能否按照真值表正确工作：

```python
# Expected Output: 1
print(gate_circuit(0, 0, 0, 0, 0))

# Expected Output: 0
print(gate_circuit(0, 0, 0, 0, 1))

# Expected Output: 0
print(gate_circuit(0, 0, 0, 1, 0))

# Expected Output: 1
print(gate_circuit(0, 0, 0, 1, 1))

# Expected Output: 1
print(gate_circuit(0, 0, 1, 0, 0))

# Expected Output: 1
print(gate_circuit(0, 0, 1, 0, 1))

# Expected Output: 0
print(gate_circuit(0, 0, 1, 1, 0))

# Expected Output: 0
print(gate_circuit(0, 0, 1, 1, 1))

# Expected Output: 1
print(gate_circuit(0, 1, 0, 0, 0))

# Expected Output: 1
print(gate_circuit(0, 1, 0, 0, 1))

# Expected Output: 1
print(gate_circuit(0, 1, 0, 1, 0))

# Expected Output: 0
print(gate_circuit(0, 1, 0, 1, 1))

# Expected Output: 0
print(gate_circuit(0, 1, 1, 0, 0))

# Expected Output: 1
print(gate_circuit(0, 1, 1, 0, 1))

# Expected Output: 0
print(gate_circuit(0, 1, 1, 1, 0))

# Expected Output: 0
print(gate_circuit(0, 1, 1, 1, 1))

# Expected Output: 0
print(gate_circuit(1, 0, 0, 0, 0))

# Expected Output: 1
print(gate_circuit(1, 0, 0, 0, 1))

# Expected Output: 1
print(gate_circuit(1, 0, 0, 1, 0))

# Expected Output: 0
print(gate_circuit(1, 0, 0, 1, 1))

# Expected Output: 0
print(gate_circuit(1, 0, 1, 0, 0))

# Expected Output: 0
print(gate_circuit(1, 0, 1, 0, 1))

# Expected Output: 0
print(gate_circuit(1, 0, 1, 1, 0))

# Expected Output: 0
print(gate_circuit(1, 0, 1, 1, 1))

# Expected Output: 0
print(gate_circuit(1, 1, 0, 0, 0))

# Expected Output: 0
print(gate_circuit(1, 1, 0, 0, 1))

# Expected Output: 0
print(gate_circuit(1, 1, 0, 1, 0))

# Expected Output: 0
print(gate_circuit(1, 1, 0, 1, 1))

# Expected Output: 0
print(gate_circuit(1, 1, 1, 0, 0))

# Expected Output: 0
print(gate_circuit(1, 1, 1, 0, 1))

# Expected Output: 0
print(gate_circuit(1, 1, 1, 1, 0))

# Expected Output: 0
print(gate_circuit(1, 1, 1, 1, 1))