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# Combining gates
From gates to a processor · Building with gates
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## Today
**We are learning to** 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.
- I can work out a circuit's output, gate by gate.
- I can build a circuit to match a truth table.
- I can explain why NAND gates can build anything.
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## Why it matters
> AND, OR and NOT are tiny. How do you get from three tiny gates to a whole processor?
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💬 Discussion
## Predict
**A and B go into an OR gate. The OR gate's output goes into a NOT gate, which lights the lamp. Both switches are off. Is the lamp on?**
- On (1): OR gives 0, and NOT flips it to 1
- Off (0): both switches are off
- Off (0): NOT only works on switches
- It depends on the order of the switches
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✍️ Activity
## Try it
{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fsystems%2Flogic%2Fcombine%2Fstep-2&code=widget%3A+gates%0Agate+g1%3A+or+A+B%0Agate+g2%3A+not+g1%0Awire+Q%3A+g2%0Alock%3A+on%0Atable%3A+tried%0A&fresh=1}}
[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/systems/logic/combine/?full=step-2#step-2)
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✅ Check
## What happened?
* On. OR of 0 and 0 is 0; the NOT gate gets that 0 and flips it to 1.
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💬 Discussion
## Gate by gate (A = 1, B = 1)
Now do the row A = 0, B = 1 for gate 3.
$$\text{gate 1: } 1 \text{ OR } 1 = 1$$
1) $\text{gate 2: } 1 \text{ AND } 1 = 1$ — Gate 2 is wired from both switches too.
2) $\text{gate 3: NOT } 1 = 0$ — Gate 3 is wired from gate 2, so it flips gate 2's output, not a switch.
3) $\text{gate 4: } 1 \text{ AND } 0 = 0$ — Gate 4 is wired from gates 1 and 3.
4) $Q = 0$ — Both on gives 0. Do every row this way to fill the truth table.
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✅ Check
## Gate by gate (A = 1, B = 1)
**In the four-gate circuit (OR, AND, NOT, AND), A = 0 and B = 1. What does gate 3, the NOT gate, output?**
* Answer: 1
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✅ Check
## Find the mistake
**Sam works out the four-gate circuit. Click the line where it first goes wrong.**
```
1 A = 1, B = 0.
2 Gate 1 (OR): 1 OR 0 = 1.
3 Gate 2 (AND): 1 AND 0 = 0.
4 Gate 3 (NOT): NOT A = NOT 1 = 0.
5 Gate 4 (AND): 1 AND 0 = 0, so Q = 0.
```
* Answer: line 4
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✅ Check
## Name it
**The four-gate circuit gives 1 when exactly one switch is on. Which gate does that on its own?**
- XOR
- AND
- NOR
- OR
* Answer: XOR
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✍️ Activity
## Vary: build to a table
- **NAND:**
- **A and not B:**
- **NOT from NAND:**
- **OR from NAND:**
[Open this step](https://studio.learningwaypoints.com/tutorials/systems/logic/combine/?full=step-4#step-4)
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✅ Check
## NOT then AND
**A goes into a NOT gate. Its output and B go into an AND gate. A = 0, B = 1. What is the output?**
- 0
- 1
* Answer: 1
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✅ Check
## NAND then NOT
**A and B go into a NAND gate; its output goes into a NOT gate. Which single gate is that the same as?**
- NOT
- OR
- NAND
- AND
* Answer: AND
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✅ Check
## Review: rows
**Review: a circuit has 3 switches. How many rows does its truth table have?**
- 3
- 6
- 8
- 9
* Answer: 8
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✍️ Activity
## Make: build XOR
Then: could you build XOR from NAND gates only? (It takes four.)
[Open this step](https://studio.learningwaypoints.com/tutorials/systems/logic/combine/?full=step-6#step-6)
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✅ Check
## Exit ticket
**A and B go into an AND gate; its output goes into a NOT gate. What is the output for A = 1, B = 1, and what is this circuit called?**
* 1 AND 1 = 1, NOT 1 = 0. It is NAND (not both).