The big idea: A digital system compares input data using logic. Every signal is 1 or 0, a group of them is a binary number, and the rules for combining them are Boolean algebra.
A combinational circuit's output depends only on the inputs NOW. A sequential circuit's output also depends on what happened BEFORE — it remembers.
Each gate with its symbol, its truth table and its rule in plain English.
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| Idea | What it is | Why it matters |
|---|---|---|
| Bit | One signal, 1 or 0, on or off | The smallest thing a digital system can store or send |
| Binary number | A group of bits: 1011 is 8 + 0 + 2 + 1 = 11 | Eight bits give 256 values, which is why an 8-bit converter has 256 steps |
| Boolean AND, OR, NOT | The three basic operations, written as a dot, a plus and a bar | Any logic function at all can be built from them, which is why they are the basic set |
| Truth table | Every input combination with the output for each | It defines a circuit completely — two inputs give four rows, three give eight |
Counting the rows: Two inputs give 2² = 4 rows. Three inputs give 2³ = 8. Four give sixteen.
An incomplete truth table is the commonest way marks are lost here, and counting the rows first prevents it.
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| Combinational | Sequential | |
|---|---|---|
| What decides the output | The inputs at this moment, and nothing else | The inputs AND the circuit's own previous state |
| Built from | Gates only | Gates plus a memory element — a latch, a flip-flop, or a counter |
| Example | A machine guard interlock: run only if the guard is down AND both buttons are pressed | A latching alarm that stays on once triggered until somebody resets it |
| Described by | A truth table | A truth table plus a state — what it does depends on where it already is |
The design question this settles: Ask whether the product must remember anything.
A press that stops when a hand leaves a button is combinational. An alarm that keeps sounding after the intruder has gone is sequential — and that difference decides whether a latch is needed at all.
How this is tested — describing digital systems in terms of binary, Boolean algebra and logic circuits. It comes up two ways:
Paper 1 — multiple choice
- Complete a row of a truth table.
- Convert a small binary number to decimal.
Paper 2 — analysing a product
- Construct a truth table for a described circuit.
- Explain why a system needs a sequential rather than a combinational circuit.
The trap: Writing an incomplete truth table. Count the rows first: two inputs give four, three give eight.
A lift door may only close when the door sensor is clear AND the button is pressed AND the lift is stationary. Construct the truth table and explain why the alarm beside it must be sequential.
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