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How do logic gates make decisions, and how do we describe and combine them?

Logic gates (AND, OR, NOT, NAND, NOR, EOR), truth tables, Boolean expressions and combinational logic for decision-making.

A CCEA A-Level Technology and Design answer on the function of AND, OR, NOT, NAND, NOR and EOR gates, their truth tables and Boolean expressions, and combining gates into decision-making combinational logic systems.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-16

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

CCEA expects you to know the function, truth table and Boolean expression of each common logic gate (AND, OR, NOT, NAND, NOR, EOR/XOR), to combine gates into combinational logic that makes decisions, and to understand that NAND and NOR are universal gates. Designing logic from a word problem is a frequent question.

The answer

The gates and their truth tables

Boolean expressions and universal gates

Combinational logic for decisions

Worked example: designing logic from a requirement

A bath-overflow and temperature alarm

An alarm must sound if the water is too high OR (too hot AND the tap is on). Inputs: high level $H$ , too hot $T$ , tap on $P$ ; output $Q$ .

step Translate the requirement to Boolean

"Too hot AND tap on" is $T \cdot P$ . "High level OR (that)" is:

Q = H + (T \cdot P).

step Choose the gates

You need one AND gate (for $T \cdot P$ ) feeding one OR gate (with $H$ ). Two gates implement the whole condition.

step Check a few rows

If $H=1$ (water high), $Q=1$ whatever else, correct. If $H=0$ , $T=1$ , $P=1$ , then $T\cdot P=1$ so $Q=1$ , correct. If $H=0$ , $T=1$ , $P=0$ , then $T\cdot P=0$ and $Q=0$ , correct (hot but tap off, no overflow risk). Translating the words to a Boolean expression and then to gates is exactly the method CCEA marks.

Examples in context

Example 1. Car seatbelt warning. The chime sounds if the ignition is ON AND a seat is occupied AND the belt is NOT fastened, a three-input AND with one inverted input, exactly the machine-guard pattern.

Example 2. Burglar alarm zones. The alarm triggers if zone 1 OR zone 2 OR zone 3 is breached while the system is armed, an OR of the zones gated by the armed signal, showing OR logic in a real product.

Try this

Q1. Write the Boolean expression for a two-input OR gate and state when its output is 0. [2 marks]

Cue. $Q = A + B$ ; the output is 0 only when both inputs are 0.

Q2. Complete the output for a two-input EOR (XOR) gate for inputs (0,0), (0,1), (1,0), (1,1). [2 marks]

Cue. 0, 1, 1, 0 - the output is 1 only when the inputs differ.

Q3. Why is NAND described as a universal gate? [1 mark]

Cue. Any logic function can be built using only NAND gates.

Exam-style practice questions

Practice questions written in the style of CCEA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

CCEA 20196 marksA machine must only operate when its guard is closed AND the start button is pressed, but it must stop immediately if an emergency stop is pressed. Design the logic, write the Boolean expression and draw the truth table for the guard and start inputs.

Show worked answer →

Let guard closed = $G$ , start pressed = $S$ , emergency stop pressed = $E$ , output (machine on) = $Q$ .

The machine runs when $G$ AND $S$ are both true, and the emergency stop is not pressed. Using NOT-E for "emergency not pressed":

Q = G \cdot S \cdot \overline{E}.

This needs a 3-input AND (or two 2-input ANDs) with the emergency-stop signal inverted by a NOT gate first (so pressing E makes $\overline{E}=0$ and forces $Q=0$ , stopping the machine).

Truth table for the guard and start inputs (with E not pressed, so $\overline{E}=1$ ):

G	S	Q
0	0	0
0	1	0
1	0	0
1	1	1

So the output is 1 only when both G and S are 1. Markers reward the AND condition, the inverted emergency-stop term, the correct Boolean expression $Q = G \cdot S \cdot \overline{E}$ , and a correct AND truth table.

CCEA 20214 marksState the Boolean expression and complete the truth table for a two-input NAND gate, and explain why NAND is called a universal gate.

Show worked answer →

A NAND gate is an AND followed by a NOT, so its output is the inverse of AND:

Q = \overline{A \cdot B}.

Truth table:

A	B	Q
0	0	1
0	1	1
1	0	1
1	1	0

The output is 0 only when both inputs are 1; otherwise it is 1.

NAND is a universal gate because any other logic function (NOT, AND, OR, NOR, etc.) can be built using only NAND gates. This means a whole logic system can be manufactured from one type of gate, simplifying production and stock. Markers want the $\overline{A \cdot B}$ expression, the correct truth table (only 1-1 gives 0), and the "any function from NAND alone" explanation.

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Sources & how we know this

CCEA GCE Technology and Design specification — CCEA (2016)