# Logic Gate

###### tags: `computerArchitecture` `digitalLogic`

> [TOC]

[Reference Video](https://www.youtube.com/watch?v=Mzy0RG9Z1Ak)

## Not

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Not.hdl

/**
 * Not gate:
 * out = not in
 */

CHIP Not {
    //declare input/output pin
    IN in;
    OUT out;

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

### Simulation

Open the simulator


Load chip

hdl File

load script

tes File


## OR

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Or.hdl

 /**
 * Or gate:
 * out = 1 if (a == 1 or b == 1)
 *       0 otherwise
 */

CHIP Or {
    IN a, b;
    OUT out;

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





## AND

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/And.hdl

/**
 * And gate: 
 * out = 1 if (a == 1 and b == 1)
 *       0 otherwise
 */

CHIP And {
    IN a, b;
    OUT out;

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

## XOR

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Xor.hdl

/**
 * Exclusive-or gate:
 * out = not (a == b)
 */

CHIP Xor {
    IN a, b;
    OUT out;

    PARTS:
    // Put your code here:

    //phase 1
    And(a=a, b=b, out=AandB);

    //phase 1
    Or(a=a, b=b, out=AorB);
    Not(in=AorB, out=notAorB);

    //phase 2
    Or(a=AandB, b=notAorB, out=output2);
    Not(in=output2, out=out);
   
}





## Multiplexer or Mul

Multiplexer just be like if-else selector.

Core concept:
Use the selector to control input input A or input B


// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Mux.hdl

/** 
 * Multiplexor:
 * out = a if sel == 0
 *       b otherwise
 */

CHIP Mux {
    IN a, b, sel;
    OUT out;

    PARTS:
    // Put your code here:
    //phase 1
    Not(in=sel, out=notSel);
    And(a=a, b=notSel, out=aAndNSel);
    And(a=b, b=sel, out=bAndNotSel);
    
    //phase 2 
    Or(a=aAndNSel, b=bAndNotSel, out=out);
    
}


## Demultiplexer


// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/DMux.hdl

/**
 * Demultiplexor:
 * {a, b} = {in, 0} if sel == 0
 *          {0, in} if sel == 1
 */

CHIP DMux {
    IN in, sel;
    OUT a, b;

    PARTS:
    Not(in=sel, out=notIn);
    And(a=in, b=notIn, out=a);
    And(a=in, b=sel, out=b);
}

## 16-bit Not

### Two-bit not gate

if we can draw two-bit not gate then we can generalize 16-bit not gate

Make input and output two bytes


// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Not16.hdl

/**
 * 16-bit Not:
 * for i=0..15: out[i] = not in[i]
 */

CHIP Not16 {
    IN in[16];
    OUT out[16];

    PARTS:
    // Put your code here:
    Not(in=in[0], out=out[0]);
    Not(in=in[1], out=out[1]);
    Not(in=in[2], out=out[2]);
    Not(in=in[3], out=out[3]);
    Not(in=in[4], out=out[4]);
    Not(in=in[5], out=out[5]);
    Not(in=in[6], out=out[6]);
    Not(in=in[7], out=out[7]);
    Not(in=in[8], out=out[8]);
    Not(in=in[9], out=out[9]);
    Not(in=in[10], out=out[10]);
    Not(in=in[11], out=out[11]);
    Not(in=in[12], out=out[12]);
    Not(in=in[13], out=out[13]);
    Not(in=in[14], out=out[14]);
    Not(in=in[15], out=out[15]);
}

## 16-bit AND

it's going to be very similar conceptual to our 16-bit Not

![Uploading file..._mdlkgkw3f]()

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/And16.hdl

/**
 * 16-bit bitwise And:
 * for i = 0..15: out[i] = (a[i] and b[i])
 */

CHIP And16 {
    IN a[16], b[16];
    OUT out[16];

    PARTS:
    // Put your code here:
    And(a=a[0], b=b[0], out=out[0]);
    And(a=a[1], b=b[1], out=out[1]);
    And(a=a[2], b=b[2], out=out[2]);
    And(a=a[3], b=b[3], out=out[3]);
    And(a=a[4], b=b[4], out=out[4]);
    And(a=a[5], b=b[5], out=out[5]);
    And(a=a[6], b=b[6], out=out[6]);
    And(a=a[7], b=b[7], out=out[7]);
    And(a=a[8], b=b[8], out=out[8]);
    And(a=a[9], b=b[9], out=out[9]);
    And(a=a[10], b=b[10], out=out[10]);
    And(a=a[11], b=b[11], out=out[11]);
    And(a=a[12], b=b[12], out=out[12]);
    And(a=a[13], b=b[13], out=out[13]);
    And(a=a[14], b=b[14], out=out[14]);
    And(a=a[15], b=b[15], out=out[15]);
    
}

## 16-bit OR

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Or16.hdl

/**
 * 16-bit bitwise Or:
 * for i = 0..15 out[i] = (a[i] or b[i])
 */

CHIP Or16 {
    IN a[16], b[16];
    OUT out[16];

    PARTS:
    or(a=a[0], b=b[0], out=out[0]);
    or(a=a[1], b=b[1], out=out[1]);
    or(a=a[2], b=b[2], out=out[2]);
    or(a=a[3], b=b[3], out=out[3]);
    or(a=a[4], b=b[4], out=out[4]);
    or(a=a[5], b=b[5], out=out[5]);
    or(a=a[6], b=b[6], out=out[6]);
    or(a=a[7], b=b[7], out=out[7]);
    or(a=a[8], b=b[8], out=out[8]);
    or(a=a[9], b=b[9], out=out[9]);
    or(a=a[10], b=b[10], out=out[10]);
    or(a=a[11], b=b[11], out=out[11]);
    or(a=a[12], b=b[12], out=out[12]);
    or(a=a[13], b=b[13], out=out[13]);
    or(a=a[14], b=b[14], out=out[14]);
    or(a=a[15], b=b[15], out=out[15]);
}

## 16-bit Mux

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Mux16.hdl

/**
 * 16-bit multiplexor: 
 * for i = 0..15 out[i] = a[i] if sel == 0 
 *                        b[i] if sel == 1
 */

CHIP Mux16 {
    IN a[16], b[16], sel;
    OUT out[16];

    PARTS:
    // Put your code here:
    Mux(a=a[0], b=b[0], sel=sel, out=out[0]); 
    Mux(a=a[1], b=b[1], sel=sel, out=out[1]);
    Mux(a=a[2], b=b[2], sel=sel, out=out[2]);
    Mux(a=a[3], b=b[3], sel=sel, out=out[3]);
    Mux(a=a[4], b=b[4], sel=sel, out=out[4]);
    Mux(a=a[5], b=b[5], sel=sel, out=out[5]);
    Mux(a=a[6], b=b[6], sel=sel, out=out[6]);
    Mux(a=a[7], b=b[7], sel=sel, out=out[7]);
    Mux(a=a[8], b=b[8], sel=sel, out=out[8]);
    Mux(a=a[9], b=b[9], sel=sel, out=out[9]);
    Mux(a=a[10], b=b[10], sel=sel, out=out[10]);
    Mux(a=a[11], b=b[11], sel=sel, out=out[11]);
    Mux(a=a[12], b=b[12], sel=sel, out=out[12]);
    Mux(a=a[13], b=b[13], sel=sel, out=out[13]);
    Mux(a=a[14], b=b[14], sel=sel, out=out[14]);
    Mux(a=a[15], b=b[15], sel=sel, out=out[15]);
}

## 8 way OR


// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Or8Way.hdl

/**
 * 8-way Or: 
 * out = (in[0] or in[1] or ... or in[7])
 */

CHIP Or8Way {
    IN in[8];
    OUT out;

    PARTS:
    // Put your code here:
    //phrase 1
    Or(a=in[0], b=in[1], out=or1);
    Or(a=in[2], b=in[3], out=or2);
    Or(a=in[4], b=in[5], out=or3);
    Or(a=in[6], b=in[7], out=or4);

    //phrase2
    Or(a=or1, b=or2, out=layer2or1);
    Or(a=or3, b=or4, out=layer2or2);

    Or(a=layer2or1, b=layer2or2, out=out);
}

## 4-Way Demux

4-way and 8-way muxes and d-muxes not actually difficult but they are complicated, it's very easily to lose yourself or lose track of what you're doing in the middle of it.


// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/DMux4Way.hdl

/**
 * 4-way demultiplexor:
 * {a, b, c, d} = {in, 0, 0, 0} if sel == 00
 *                {0, in, 0, 0} if sel == 01
 *                {0, 0, in, 0} if sel == 10
 *                {0, 0, 0, in} if sel == 11
 */

CHIP DMux4Way {
    IN in, sel[2];
    OUT a, b, c, d;

    PARTS:
    // Put your code here:

    //phase 1

    DMux(in=in, sel=sel[1], a=DmuxA1, b=DmuxB1);

    //pahse 2
    DMux(in=DmuxA1, sel=sel[0], a=a, b=b);
    DMux(in=DmuxB1, sel=sel[0], a=c, b=d);
}

8-Way Demux

this is the four-way d-mux only even more, I'm not to going to draw this one

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/DMux8Way.hdl

/**
 * 8-way demultiplexor:
 * {a, b, c, d, e, f, g, h} = {in, 0, 0, 0, 0, 0, 0, 0} if sel == 000
 *                            {0, in, 0, 0, 0, 0, 0, 0} if sel == 001
 *                            etc.
 *                            {0, 0, 0, 0, 0, 0, 0, in} if sel == 111
 */

CHIP DMux8Way {
    IN in, sel[3];
    OUT a, b, c, d, e, f, g, h;

    PARTS:
    DMux(in=in, sel=sel[2], a=abcd, b=efgh);
    DMux4Way(in=abcd, sel=sel[0..1], a=a, b=b, c=c, d=d);
    DMux4Way(in=efgh, sel=sel[0..2], a=e, b=f, c=g, d=h);
}

4way 16-bit demux

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Mux4Way16.hdl

/**
 * 4-way 16-bit multiplexor:
 * out = a if sel == 00
 *       b if sel == 01
 *       c if sel == 10
 *       d if sel == 11
 */

CHIP Mux4Way16 {
    IN a[16], b[16], c[16], d[16], sel[2];
    OUT out[16];

    PARTS:
    Mux16(a=a, b=b, sel=sel[0], out=mux1Out);
    Mux16(a=c, b=d, sel=sel[0], out=mux2Out);
    Mux16(a=mux1Out, b=mux2Out, sel=sel[1], out=out);
    
}

8 way 16-bit mux

It's very simple, since it just reverse logic with 8 way 16-bit demux which have implemented.

Basically, we just flip it and then we can get the answer.

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/Mux8Way16.hdl

/**
 * 8-way 16-bit multiplexor:
 * out = a if sel == 000
 *       b if sel == 001
 *       etc.
 *       h if sel == 111
 */

CHIP Mux8Way16 {
    IN a[16], b[16], c[16], d[16],
       e[16], f[16], g[16], h[16],
       sel[3];
    OUT out[16];

    PARTS:
    // Put your code here:
    Mux4Way16(a=a, b=b, c=c, d=d, sel=sel[0..1], out=Mux1Output);
    Mux4Way16(a=e, b=f, c=g, d=h, sel=sel[0..1], out=Mux2Output);
    Mux16(a=Mux1Output, b=Mux2Output, sel=sel[2], out=out);
}