Lesson 1. Gates and the half adder: 1 + 1 = 10

After this lesson two lamps will show the sum of two bits: 1 + 1 lights up as 10 — "two" in binary. Along the way we build all the gates of the kit from transistors: NOT, NAND, NOR, AND, OR and XOR. The rest of the kit is built only from them.

1.1. The idea: adding one digit

A binary digit has only two values, so adding one digit is just four cases:

Look at the columns one at a time:

• S = A ⊕ B — lit when exactly one input is lit. That is "exclusive OR", XOR;
• C = A · B — lit when both are lit. That is AND.

A unit made of XOR and AND is called a half adder (HA). "Half" because it adds two bits but cannot take a carry from the neighbouring digit. The full adder in lesson 2 does that.

The kit's XOR is made of ready gates: "at least one" (OR) and at the same time "not both" (NAND) — XOR = AND(OR, NAND).

1.2. Building

A new empty project. First place the power: Power → label VCC, Ground → label GND (they are shared inside chips). Each gate is built on an empty spot of the canvas, then select its parts with their labels → Ctrl+G → double-click the name in the library → the chip name. Transistor: the gate G on the left, the channel is top and bottom (interchangeable); pmos conducts when the gate is 0, nmos when it is 1.

If you already have NOT and AND from the "Character Generator" kit — use them, they are the same. Gates from the "A Watch and a Game from Gates" kit will do too: their pins A, B, Y are the same as I0, I1, O0 in the tables.

Step 1. NOT — flip: 1 → 0, 0 → 1

Ctrl+G → name NOT.

A common mistake. Swapping N and P: if N is on top (to VCC) and P at the bottom (to GND), the gate does not flip but repeats its input. P always goes on top, N at the bottom. The type changes with Alt + click on the transistor (on a Mac — ⌥ or ⌘ + click); a plain click does not change it.

Step 2. NAND — NOT-AND: 0 only when both inputs are 1

Ctrl+G → name NAND.

Step 3. NOR — NOT-OR: 1 only when both inputs are 0

Ctrl+G → name NOR.

Step 4. AND: NAND at node n, then a flip

Ctrl+G → name AND.

Step 5. OR: NOR at node n, then a flip

Ctrl+G → name OR.

Step 6. XOR — "at least one, but not both"

From ready gates: XOR = AND(OR, NAND).

Ctrl+G → name XOR.

Step 7. HA — the half adder

The sum of one digit S = A ⊕ B and the carry C = A · B.

Ctrl+G → name HA. Chip pins: inputs A, B, outputs S, C.

Step 8. Canvas: switches, half adder, lamps

Put the lamps side by side: C on the left, S on the right — that way they read as a binary number.

1.3. Check

If S is lit at 1 + 1, check XOR: its NAND must give 0 when both inputs are 1.

Lesson 1 paste (Cmd+I)

A new empty project. The paste places all the gates, the half adder and the lesson setup.

# Lesson 1 — the kit gates from transistors and the half adder HA.chip NOT {  portIn(I0)  portOut(O0)  pmos(I0, VCC, O0)  nmos(I0, O0, GND)} chip NAND {  portIn(I0)  portIn(I1)  portOut(O0)  pmos(I0, VCC, O0)  pmos(I1, VCC, O0)  nmos(I0, O0, mid)  nmos(I1, mid, GND)} chip NOR {  portIn(I0)  portIn(I1)  portOut(O0)  pmos(I0, VCC, mid)  pmos(I1, mid, O0)  nmos(I0, O0, GND)  nmos(I1, O0, GND)} chip AND {  portIn(I0)  portIn(I1)  portOut(O0)  pmos(I0, VCC, n)  pmos(I1, VCC, n)  nmos(I0, n, mid)  nmos(I1, mid, GND)  pmos(n, VCC, O0)  nmos(n, O0, GND)} chip OR {  portIn(I0)  portIn(I1)  portOut(O0)  pmos(I0, VCC, mid)  pmos(I1, mid, n)  nmos(I0, n, GND)  nmos(I1, n, GND)  pmos(n, VCC, O0)  nmos(n, O0, GND)} chip XOR {  portIn(I0)  portIn(I1)  portOut(O0)  OR(I0, I1, o)  NAND(I0, I1, n)  AND(o, n, O0)} chip HA {  portIn(A)  portIn(B)  portOut(S)  portOut(C)  XOR(A, B, S)  AND(A, B, C)} power(VCC)ground(GND)input(A)input(B)HA(A, B, S, C)led(S)led(C)