서론 + Nand2Tetris Chapter 1

서론

Nand라는 논리 연산 하나에서 시작해 테트리스 게임을 만드는 프로젝트 Nand2Tetris! 이 프로젝트의 개념을 정리하기엔 너무 힘들 것 같아서 인증 및 과제를 기록하는 칸으로 활용할 예정이다. 

 

Nand2Tetris :  https://www.coursera.org/learn/build-a-computer

Build a Modern Computer from First Principles: From Nand to Tetris (Project-Centered Course)

---

Chapter 1

Boolean Functions and Gate Logic

만들어야하는 Boolean 함수들

Chapter 1에서는 Nand를 이용해 여러 Boolean 함수를 만들어야 한다.

---

1. Not

CHIP Not {
    IN in;
    OUT out;

    PARTS:
    Nand (a=in, b=in, out=out);
}

 

2. And

CHIP And {
    IN a, b;
    OUT out;

    PARTS:
    Nand (a=a, b=b, out=aNandb);
    Nand (a=aNandb, b=aNandb, out=out);
}

 

3. Or

CHIP Or {
    IN a, b;
    OUT out;

    PARTS:
    Nand (a=a, b=a, out=Nota);
    Nand (a=b, b=b, out=Notb);
    Nand (a=Nota, b=Notb, out=out);
}

 

4. 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:
    Not (in=a, out=Nota);
    Not (in=b, out=Notb);
    And (a=Nota, b=b, out=notaAndb);
    And (a=a, b=Notb, out=aAndnotb);
    Or (a=notaAndb, b=aAndnotb, out=out);
}

 

5. 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/Mux.hdl

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

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

    PARTS:
    Not (in=sel, out=Notsel);
    And (a=a, b=Notsel, out=x);
    And (a=b, b=sel, out=y);
    Or (a=x, b=y, out=out);
}

 

6. DMux

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

 

7. Not16

// 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:
    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]);
}

 

8. And16

// 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:
    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]);
}

 

9. Or16

// 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]);
}

 

10. Mux16

// 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:
    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]);
}

 

11. Or8Way

// 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:
    Or (a=in[0],b=in[1],out=x1);
	Or (a=x1,b=in[2],out=x2);
	Or (a=x2,b=in[3],out=x3);
	Or (a=x3,b=in[4],out=x4);
	Or (a=x4,b=in[5],out=x5);
	Or (a=x5,b=in[6],out=x6);
	Or (a=x6,b=in[7],out=out);
}

 

12. Mux4Way16

// 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=x);
    Mux16 (a=c, b=d, sel=sel[0], out=y);
    Mux16 (a=x, b=y, sel=sel[1], out=out);
}

 

13. Mux8Way16

// 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:
    Mux4Way16 (a=a, b=b, c=c, d=d, sel=sel[0..1], out=x);
    Mux4Way16 (a=e, b=f, c=g, d=h, sel=sel[0..1], out=y);
    Mux16 (a=x, b=y, sel=sel[2], out=out);
}

 

14. DMux4Way

// 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:
	DMux (in=in, sel=sel[0], a=x, b=y);
	DMux (in=in, sel=sel[1], a=x2, b=y2);
	And (a=x, b=x2, out=a);
    And (a=y, b=x2, out=b);
	And (a=x, b=y2, out=c);
	And (a=y, b=y2, out=d);
}

 

15. DMux8Way

// 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:
    DMux4Way (in=in, sel=sel[0..1], a=x, b=x2, c=x3, d=x4);
	DMux (in=in, sel=sel[2], a=y, b=y2);
	And (a=x, b=y, out=a);
	And (a=x2, b=y, out=b);
	And (a=x3, b=y, out=c);
	And (a=x4, b=y, out=d);
	And (a=x, b=y2, out=e);
	And (a=x2, b=y2, out=f);
	And (a=x3, b=y2, out=g);
	And (a=x4, b=y2, out=h);
}