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How do you turn a set of requirements into a working logic circuit, and why are NAND and NOR universal?

Designing combinational logic: building a circuit from a truth table or word description, combining gates, and the universal NAND and NOR gates.

An Eduqas GCSE Electronics answer on designing combinational logic: turning a word description or truth table into a Boolean expression and a gate circuit, combining gates into a system, and using the universal NAND and NOR gates to build any function from one gate type.

Generated by Claude Opus 4.813 min answerUpdated 2026-06-02

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

Eduqas wants you to design a combinational logic circuit: turn a word description or a truth table into a Boolean expression and then a gate circuit, combine gates into a working system, and explain the universal NAND and NOR gates (any logic function can be built from one gate type). This is where the gates and algebra of the previous topics are put to use.

The answer

Combinational logic

Designing from a description or truth table

Combining gates into a system

Universal gates

Designing a two-out-of-three voting circuit

Design a circuit whose output is 1 when at least two of three inputs $A$ , $B$ , $C$ are 1.

step 1: Write the conditions for a 1 output

The output is 1 when any pair is high: $A$ and $B$ , or $A$ and $C$ , or $B$ and $C$ . As an expression: $\text{out} = A \cdot B + A \cdot C + B \cdot C$ .

step 2: Identify the gates

Three two-input AND gates form the pairs $A \cdot B$ , $A \cdot C$ and $B \cdot C$ ; a three-input OR gate (or two two-input ORs) combines them.

step 3: Check a sample row

For $A,B,C = 1,1,0$ : $A \cdot B = 1$ , so the OR output is 1 (correct, two inputs are high). For $1,0,0$ : all three ANDs are 0, so the output is 0 (correct, only one input is high).

Examples in context

Designing combinational logic is the core skill of the digital part of the course and of the non-exam assessment. A machine guard interlock, a two-out-of-three voting safety system, a code lock and a seven-segment decoder are all combinational designs built from a truth table or a word description. Building everything from NAND gates shows why one chip type can implement a whole design, and the same approach feeds into the adders and arithmetic circuits that follow.

Try this

Q1. State what "combinational" means for a logic circuit. [1 mark]

Cue. The output depends only on the present inputs (it has no memory).

Q2. Write a Boolean expression for an output that is 1 when $A$ and $B$ are both 1, or when $C$ is 1. [2 marks]

Cue. $A \cdot B + C$ .

Q3. State how to make a NOT gate from a single NAND gate. [1 mark]

Cue. Tie both NAND inputs together (a NAND of $A$ with $A$ gives $\overline{A}$ ).

Exam-style practice questions

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

Eduqas 20195 marksA machine should sound an alarm when a guard is open (

A = 1

) and the motor is running (

B = 1

), or when an emergency stop is pressed (

C = 1

). Write a Boolean expression for the alarm output and describe the gates needed.

Show worked answer →

Expression (up to 3 marks): the guard-and-motor condition is $A \cdot B$ ; the emergency stop is $C$ ; the alarm sounds for either, so $\text{Alarm} = A \cdot B + C$ .

Gates (up to 2 marks): an AND gate combines $A$ and $B$ ; an OR gate combines the AND output with $C$ ; the OR output drives the alarm (through a transistor switch).

Markers reward the correct expression $A \cdot B + C$ and a description using one AND and one OR gate (the order and roles correct).

Eduqas 20224 marksExplain what is meant by a universal gate, and show how a NOT gate and an AND gate can each be made from NAND gates only.

Show worked answer →

Universal gate (up to 2 marks): a universal gate is one from which any logic function can be built; NAND and NOR are both universal, so a whole circuit can be made from one gate type.

Constructions (up to 2 marks): a NOT gate is a NAND with both inputs joined together (a NAND of $A$ with $A$ gives $\overline{A}$ ). An AND gate is a NAND followed by this NAND-inverter, because inverting the NAND output $\overline{A \cdot B}$ gives $A \cdot B$ .

Markers reward the definition (any function from one gate type) and both valid constructions (NOT from a NAND with tied inputs, AND from a NAND plus an inverter).

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Sources & how we know this

WJEC Eduqas GCSE (9-1) Electronics specification (C490) — WJEC Eduqas (2017)