0291-Nand-实现基础逻辑门（一）

环境

• Time 2023-07-06

前言

说明

参考：https://www.nand2tetris.org/

目标

通过最基础的 Nand（与非门）实现 Not、And、Or、Xor、Mux、DMux 几个基础门。

Not

/**
 * Not gate:
 * out = not in
 */
/** Sets out = in Nand in */
CHIP Not {
    IN in;
    OUT out;

    PARTS:
    // Put your code here:
    Nand(a = in, b = in, out = out);
}

And

/**
 * And gate:
 * out = 1 if (a == 1 and b == 1)
 *       0 otherwise
 */
/** Sets out = Not(a Nand b) */
CHIP And {
    IN a, b;
    OUT out;

    PARTS:
    // Put your code here:
    Nand(a = a, b = b, out=aNandb);
    Not(in = aNandb, out = out);
}

Or

 /**
 * Or gate:
 * out = 1 if (a == 1 or b == 1)
 *       0 otherwise
 */
/** Sets out = Not(Not(a) And Not(b)) */
CHIP Or {
    IN a, b;
    OUT out;

    PARTS:
    // Put your code here:
    Not(in = a, out = Nota);
    Not(in = b, out = Notb);
    And(a = Nota, b = Notb, out = NotaAndNotb);
    Not(in = NotaAndNotb, out = out);
}

Xor

/**
 * Exclusive-or gate:
 * out = not (a == b)
 */
/** Sets out = ((a And Not(b)) Or (Not(a) And b)) */
CHIP Xor {
    IN a, b;
    OUT out;

    PARTS:
    // Put your code here:
    Not(in = b, out = Notb);
    And(a = a, b = Notb, out = aAndNotb);

    Not(in = a, out = Nota);
    And(a = Nota, b = b, out = NotaAndb);

    Or(a = aAndNotb, b = NotaAndb, out = out);
}

Mux

/**
 * Multiplexor:
 * out = a if sel == 0
 *       b otherwise
 */
/** Sets out = ((a And Not(sel)) Or (b And sel)) */
CHIP Mux {
    IN a, b, sel;
    OUT out;

    PARTS:
    // Put your code here:
    Not(in = sel, out = Notsel);
    And(a = a, b = Notsel, out = aAndNotsel);

    And(a = b, b = sel, out = bAndsel);
    Or(a = aAndNotsel, b = bAndsel, out = out);
}

DMux

/**
 * Demultiplexor:
 * {a, b} = {in, 0} if sel == 0
 *          {0, in} if sel == 1
 */
/** Sets a = (in And (Not(sel))) */
/** Sets b = (in And sel) */
CHIP DMux {
    IN in, sel;
    OUT a, b;

    PARTS:
    // Put your code here:
    Not(in = sel, out = Notsel);
    And(a = in, b = Notsel, out = a);

    And(a = in, b = sel, out = b);
}

总结

使用 Nand 这一个最基础的逻辑门，实现其它的基础逻辑门。

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