Building Own Computer with Nand2Tetris: Project I
![Building Own Computer with Nand2Tetris: Project I](https://digitalpress.fra1.cdn.digitaloceanspaces.com/r9xsadw/2022/03/Screenshot-from-2022-03-09-19-36-36.png)
I should create every logic gate from using only NAND or previously built gates. In the course, HDL language is its own type – but similar to VHDL, the instructor says.
AND Gate
![](https://digitalpress.fra1.cdn.digitaloceanspaces.com/r9xsadw/2022/03/AND.png)
// 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:
Nand (a=a, b=b, out=notAB);
Nand(a=notAB, b=notAB, out=out);
}
NOT Gate
![](https://digitalpress.fra1.cdn.digitaloceanspaces.com/r9xsadw/2022/03/NOT.png)
// 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 {
IN in;
OUT out;
PARTS:
Nand (a=in, b=in, out=out);
}
OR Gate
![](https://digitalpress.fra1.cdn.digitaloceanspaces.com/r9xsadw/2022/03/OR.png)
// 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:
Not (in=a, out=notA);
Not (in=b, out=notB);
Nand (a=notA, b=notB, out=out);
}
XOR Gate
![](https://digitalpress.fra1.cdn.digitaloceanspaces.com/r9xsadw/2022/03/XOR.png)
// 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=a, b=notB, out=o1);
And (a=notA, b=b, out=o2);
Or (a=o1, b=o2, out=out);
}
MUX (Multiplexer) Gate
![](https://digitalpress.fra1.cdn.digitaloceanspaces.com/r9xsadw/2022/03/MUX.png)
// 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=o1);
And (a=sel, b=b, out=o2);
Or (a=o1, b=o2, out=out);
}
DMux (Demultiplexer) Gate
![](https://digitalpress.fra1.cdn.digitaloceanspaces.com/r9xsadw/2022/03/DMUX.png)
// 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=notSel, b=in, out=a);
And (a=in, b=sel, out=b);
}
16-bit Gates
Since that all the logic behind the construction of one-bit and sixteen-bit gates are the same, but the number of gate huge, I won't put the schematics and Logism circuit files in this section.
Not16
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]);
}
And16
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]);
}
Or16
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]);
}
Mux16
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]);
}
Multi-way Variants
In this section, we're going to construct Mux and DMux gates with more than two input channels.
Or8Way
/**
* 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=out1);
Or (a=out1, b=in[2], out=out2);
Or (a=out2, b=in[3], out=out3);
Or (a=out3, b=in[4], out=out4);
Or (a=out4, b=in[5], out=out5);
Or (a=out5, b=in[6], out=out6);
Or (a=out6, b=in[7], out=out);
}
Mux4Way16
/**
* 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:
Not (in=sel[1], out=notSel0);
And (a=notSel0, b=sel[0], out=muxSel1);
And (a=sel[1], b=sel[0], out=muxSel2);
Mux16 (a=a, b=b, sel=muxSel1, out=out1);
Mux16 (a=c, b=d, sel=muxSel2, out=out2);
Mux16 (a=out1, b=out2, sel=sel[1], out=out);
}
Mux8Way16
/**
* 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=MuxOut1);
Mux4Way16 (a=e, b=f, c=g, d=h, sel=sel[0..1], out=MuxOut2);
Mux16 (a=MuxOut1, b=MuxOut2, sel=sel[2], out=out);
}
DMux4Way
/**
* 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[1], a=O1, b=O2);
DMux (in=O1, sel=sel[0], a=a, b=b);
DMux (in=O2, sel=sel[0], a=c, b=d);
}
DMux8Way
/**
* 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=O1, b=O2);
DMux4Way (in=O1, sel=sel[0..1], a=a, b=b, c=c, d=d);
DMux4Way (in=O2, sel=sel[0..1], a=e, b=f, c=g, d=h);
}