Mux Gate

Truth Table
a b sel | f(a,b,sel)
---------------------
0 0 0   | 0
0 0 1   | 0
0 1 0   | 0
0 1 1   | 1
1 0 0   | 1
1 0 1   | 0
1 1 0   | 1
1 1 1   | 1

Boolean Expression


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

    PARTS:
    Not(in=sel, out=selNot);
    And(a=selNot, b=a, out=out1);
    And(a=sel, b=b, out=out2);
    Or(a=out1, b=out2, out=out);
}
----------------------------------------

Or16 Gate

Truth Table
a[x] | b[x] | f(a[x],b[x])
----------------------------
0      | 0     | 0
0      | 1     | 1
1      | 0     | 1
1      | 1     | 1

--------------------------------------------------
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]);
}
--------------------------------------------------

Again you just take 2 arrays of 16 bits and OR each set of 2 bits from each array with the same index.

And16 Gate

Truth Table
a[x] | b[x] | f(a[x],b[x])
----------------------------
0      | 0     | 0
0      | 1     | 0
1      | 0     | 0
1      | 1     | 1

--------------------------------------------------
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]);
}
--------------------------------------------------

Same as the 1 bit AND gate but you take 2 sets of 16 bits and AND each set of 2 bits from each array with the same index.

Not16 Gate

Truth Table
in[x] | f(in[x])
-----------------
0       | 1
1       | 0

----------------------------------------
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]);
}
----------------------------------------

Not too much different then a 1 bit NOT gate you just take 2 sets of 16 bits and NOT each set of 2 bits from each array with the same index.

Xor Gate

Truth Table
a b | f(a,b)
------------
0 0 | 0
0 1 | 1
1 0 | 1
1 1 | 0

Boolean Expression
(!x*y)+(x*!y)

----------------------------------------

CHIP Xor
{
    IN a, b;
    OUT out;

    PARTS:
    Not(in=a, out=aNot);
    Not(in=b, out=bNot);
    And(a=aNot, b=b, out=out1);
    And(a=a, b=bNot, out=out2);
    Or(a=out1, b=out2, out=out);
}

----------------------------------------

Another that might seem hard at first but adding a few gates together does the trick.  Seeing as you want to know when its one or the other and not both the first and gate returns a 1 only if y is 1 and x is not, and the second does the the opposite returns a 1 if x is 1 and y is not.  Then its just a matter of outputing a 1 if either AND gate returned a 1.

Or Gate

Truth Table
a b | f(a,b)
------------
0 0 | 0
0 1 | 1
1 0 | 1
1 1 | 1

Boolean Expresions
a+b

---------------------------------------------
CHIP Or
{
    IN a, b;
    OUT out;

    PARTS:
    Not(in=a, out=aNot);
    Not(in=b, out=bNot);
    Nand(a=aNot, b=bNot, out=out);
}
---------------------------------------------

At first this one might seem difficult but since we have the NAND gate the opposite of what we want we just take the opposite of each in and then NAND the results.

And Gate

Truth Table
a b | f(a,b)
-------------
0 0 | 0
0 1 | 0
1 0 | 0
1 1 | 1

Boolean Expression
x*y

----------------------------------------
CHIP And
{
    IN a, b;
    OUT out;

    PARTS:
    Nand(a=a, b=b, out=out1);
    Not(in=out1, out=out);
}
----------------------------------------

Seeing as we started with the opposite of this gate the NAND and that we just created the NOT gate its as simple as taking the opposite(NOT) of the NAND gate.

Not Gate

Truth Table
in | f(in)
--------
0  | 1
1  | 0

Boolean Expressions
!x

----------------------------------------
CHIP Not
{
    IN in;
    OUT out;

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

Fairly simple gate
For TRUE(1), TRUE and TRUE is TRUE making the NAND gate return FALSE(0)
For FALSE(0, FALSE and FALSE is FASLE making the NAND gate return TRUE(0)
Out Becomes the opposite of in.

Nand2Tetris Hardware Simulator