NAND Gate 又叫与非门,可以理解为与门和非门的组合,用逻辑表达式为:
NAND as NOT
NOT 是一个单输入的逻辑门,用逻辑表达式为: 。
因为 所以
/**
* Not gate:
* out = not in
*/
CHIP Not {
IN in;
OUT out;
PARTS:
// Put your code here:
Nand(a = in, b = in, out = out);
}
NAND as AND
AND Gate 是一个两输入的逻辑门,用逻辑表达式为:, 其中 和 分别是输入的两个端口。
NAND Gate 逻辑表达式为: ,我们想要得到 ,只需要对 做一个取反操作即可,即:
/**
* And gate:
* out = a and b
*/
CHIP And {
IN a, b;
OUT out;
PARTS:
// Put your code here:
Nand(a = a, b = b, out = nandOut);
Nand(a = nandOut, b = nandOut, out = out); // Not(in = nandOut, out = out);
NAND as OR
OR Gate 是一个两输入的逻辑门,用逻辑表达式为:, 其中 和 分别是输入的两个端口。
NAND Gate 逻辑表达式为: ,根据 DeMorgan's law,我们可以得到 ,那如果我们在输入 和 的时候,分别对他们进行取反操作让输入变成 和 , 则可得到:
/**
* Or gate:
* out = a or b
*/
CHIP Or {
IN a, b;
OUT out;
PARTS:
// Put your code here:
Nand(a = a, b = a, out = nota);
Nand(a = b, b = b, out = notb);
Nand(a = nota, b = notb, out = out);
}
NAND as NOR
NOR Gate 是一个两输入的逻辑门,用逻辑表达式为:, 其中 和 分别是输入的两个端口。
上面已经有了 OR 的实现和 NOT 的实现,直接用 OR 和 NOT 就可以得到 NOR 的实现,即:
/**
* Nor gate:
* out = a nor b
*/
CHIP Nor {
IN a, b;
OUT out;
PARTS:
// Put your code here:
//Or(a = a, b = b, out = out);
Nand(a = a, b = a, out = nota);
Nand(a = b, b = b, out = notb);
Nand(a = nota, b = notb, out = orOut);
Nand(a = orOut, b = orOut, out = out);
NAND as XOR
XOR Gate 是一个两输入的逻辑门,用逻辑表达式为:, 其中 和 分别是输入的两个端口。
这里我们需要用到两个 AND,两个 NOT,一个 OR,所以一共需要九个Nand,即:
/**
* Xor gate:
* out = a xor b
*/
CHIP Xor {
IN a, b;
OUT out;
PARTS:
// Put your code here:
Nand(a = b, b = b, out = notb);
Nand(a = a, b = notb, out = nandanotb);
Nand(a = nandab, b = nandab, out = aandnotb);
Nand(a = a, b = a, out = nota);
Nand(a = nota, b = b, out = nandnotab);
Nand(a = nandnotab, b = nandnotab, out = notaandb);
Nand(a = aandnotb, b = aandnotb, out = NOTaandnotb);
Nand(a = notaandb, b = notaandb, out = NOTnotaandb);
Nand(a = NOTaandnotb, b = NOTnotaandb, out = out);
}
这个实现用到了过多的 NAND,我们想办法优化一下,注意观察图中红框里的部分,这部分是明显就是两次 NOT: 这两次 NOT 叠加之后就相当于什么事情都没干,所以我们可以把这部分干掉,就剩下五个 Nand,即: 其实我们还可以对这个门进行一次简化,用四个 NAND 来实现 XOR(这里如果全部用逻辑运算写的话太复杂,我直接在公式里使用 NAND 了):
/**
* Xor gate:
* out = a xor b
*/
CHIP Xor {
IN a, b;
OUT out;
PARTS:
// Put your code here: Nand(a = a, b = b, out = nandAB);
Nand(a = a, b = nandAB, out = nandABA);
Nand(a = b, b = nandAB, out = nandABB);
Nand(a = nandABA, b = nandABB, out = out);