Wire one gate's output into another gate's input and you get a circuit. Work a circuit out row by row, each gate using only what arrives on its wires, then build circuits to match truth tables, even from NAND gates alone.
AND, OR and NOT are tiny. How do you get from three tiny gates to a whole processor?
In Why binary: logic gates each gate stood alone. Now wire them together: one gate's output becomes another gate's input. A few simple gates combined can make any truth table you like.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
OR, then NOT
TryTry it on the board and compare the result with your prediction.
Try: follow the wires
Was your prediction right?
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Flip the switches to try all four rows. When is the lamp on?
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Worked example: row by row
Worked exampleBefore each step, say what you think comes next.
gate 1: 1 OR 1=1Gate 1 is wired from both switches.
gate 2: 1 AND 1=1Gate 2 is wired from both switches too.
gate 3: NOT 1=0Gate 3 is wired from gate 2, so it flips gate 2's output, not a switch.
gate 4: 1 AND 0=0Gate 4 is wired from gates 1 and 3.
Q=0Both on gives 0. Do every row this way to fill the truth table.
Now do the row A = 0, B = 1 for gate 3.
In the four-gate circuit (OR, AND, NOT, AND), A = 0 and B = 1. What does gate 3, the NOT gate, output?
Sam works out the four-gate circuit. Click the line where it first goes wrong.
ModifyChange the problem on purpose and see what happens.
Vary: build to a table
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Add gates and wire them so every row matches the wanted column (NAND: not both). Click a ● to wire from, then a pin to wire to.
Use the board. This ticks when you get there.
Now the lamp should light only when A is on and B is off.
Use the board. This ticks when you get there.
Only NAND gates this time, and one switch. Make a NOT. (Hint: both inputs can come from A.)
Use the board. This ticks when you get there.
Only NAND gates. Make OR.
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Read the circuit
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Build XOR
Then: could you build XOR from NAND gates only? (It takes four.)
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Need a hint?
XOR is 1 for "A or B", but not when both are on.
Another hint
One gate for "A or B", one for "both", then flip "both".
Another hint
OR, AND, NOT, then AND the OR with the NOT.
Build XOR (exactly one switch on) from AND, OR and NOT gates.
Use the board. This ticks when you get there.
For teachers
Students follow wired circuits row by row, then build circuits to match truth tables, including NOT and OR from NAND gates alone and XOR from AND, OR and NOT (AC9TDI8K04 node 3, extended; the kit names adder circuits as going further). About 45 minutes.
Try the boards yourself; wire by clicking a ● (from) then a pin (to), and click a wired pin to unplug it.
The one idea: each gate uses only what arrives on its own wires. Data representation's Why binary: logic gates is assumed (AND, OR, NOT, truth tables); start with a two-minute recap if the class hasn't done it recently.
This course is an extension (Years 9–10). Its lessons are tagged AC9TDI8K04 node 3 (why binary: circuits and logic gates), which the kit says adder circuits go further from.
Unplugged first works well: students as gates holding cards, passing 0s and 1s along strings.
Running the lesson
Predict: students who said off are reading the switches, not the OR gate's output.
Try: ask what one word describes this circuit (NOR, not-OR).
Worked example: model the order: a gate can only be worked out once everything wired into it is known.
Vary: after NOT from NAND, ask what A NAND A means in words.
Make: compare circuits: did anyone use fewer gates?
The hard part (on purpose)
Wiring is fiddly at first and the first circuits don't match. Let the wanted column's crosses do the telling: students change one wire and watch which rows turn green.
When students get stuck
A student feeds the switches into every gate in their head (Sam's mistake). Ask: Follow gate 3's wire back. Where does it start? Fix: Each gate uses its own wires only.
A student can't start building. Ask: Which rows need a 1? What do those rows have in common? Fix: Build the gate for that pattern, then fix the rows that are wrong.
Stretch and support
Stretch: Build XOR from four NAND gates. Then: why would a chip factory rather make one kind of gate?
Support: Truth table cards for AND, OR, NOT and NAND to keep on the desk.
Where it leads
Next: Adding with gates (half and full adders).
Links: Data representation › Why binary: logic gates (the introduction). For keen students and teachers, the free course From NAND to Tetris (nand2tetris.org) builds a whole computer from NAND gates.
What each step is for
OR, then NOT: Committing to the output of a two-gate circuit tests the new move: the second gate uses what the first gate gives it.
Try: follow the wires: Trying all four rows on the wired circuit settles the prediction and shows the new move: each gate works on what reaches it.
Worked example: row by row: Working a four-gate circuit one gate at a time models the new move. Sam feeds a switch into a gate that is wired to another gate, the misconception planted after the method.
Vary: build to a table: Each task changes one thing about the target: NAND from AND and NOT, A AND NOT B, then NOT and OR from NAND gates alone (a gate input may take the same wire twice).
read the circuit: Reading circuits without the board is the same move in mixed forms, plus a review of how many rows a truth table has.
build XOR: Building XOR from its truth table reverses the process: start from the wanted outputs and choose and wire the gates.