The big idea: A digital system uses discrete values — in practice two: on and off, high and low, 1 and 0. One of them is a bit.
Everything a digital system stores, processes or communicates is a pattern of those bits, and a logic gate is the circuit that decides one output bit from its input bits.
Each gate with its symbol, its truth table and the rule in plain English — which is the form a design question is asked in.
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| Gate | The rule, in English | A product that needs exactly that |
|---|---|---|
| NOT | The output is the OPPOSITE of the input | Inverting a sensor that reads low when it should read high |
| AND | The output is on only when BOTH inputs are on | A microwave that runs only when the door is closed AND start is pressed |
| OR | The output is on when EITHER input is on | An alarm that sounds if the front door OR a window opens |
| NAND | The output is on unless BOTH inputs are on | A press that stops the moment both hands leave the safety buttons |
| NOR | The output is on only when BOTH inputs are off | A pump that runs only when neither float switch is triggered |
| XOR | The output is on when the inputs are DIFFERENT | A stair light switched from either end |
The truth table IS the definition: Because each input has only two states, the table lists every possible case — so there is nothing about a gate that the table leaves unsaid.
In an exam, write the table and then read the rule off it. That is more reliable than remembering six rules.
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| A hard-wired gate | A microcontroller |
|---|---|
| Responds instantly — nanoseconds, with no program to run first | Responds in microseconds or milliseconds, after its program reaches that line |
| Cannot crash, hang or be updated into a fault | Runs software, so it can crash and it can be broken by an update |
| Costs pennies, and its behaviour is fixed by the wiring | Costs more, and its behaviour is whatever the program says |
| Changing the behaviour means changing the board | Changing the behaviour is an edit and a reload |
Which is why safety interlocks are often hard-wired: A guard interlock on a machine, or the pair of buttons on a press, is usually wired from gates or relays rather than programmed.
It has to work when the software does not — which is a design argument, not a cost one.
How this is tested — describing digital systems with discrete values, and defining logic gates. It comes up two ways:
Paper 1 — multiple choice
- Complete a row of a truth table.
- Choose the gate that matches a stated requirement.
Paper 2 — analysing a product
- Define a named logic gate and give a product that uses it.
- Explain why a safety function was built from gates rather than software.
The trap: Describing a gate without its truth table or its English rule. "An AND gate combines two inputs" says nothing; "the output is on only when both inputs are on" is the definition.
A workshop guillotine may only operate when its guard is down AND both of the operator's hands are on separate buttons. Explain the logic and why it is hard-wired.
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