What do the logic gates do, and how is each one described by a truth table?
Logic gates: AND, OR, NOT, NAND, NOR and XOR, their symbols and truth tables, and the digital high and low logic levels.
An Eduqas GCSE Electronics answer on logic gates: the AND, OR, NOT, NAND, NOR and XOR gates with their symbols and truth tables, the meaning of logic high and logic low, and how a truth table lists the output for every combination of inputs.
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What this dot point is asking
Eduqas wants you to know the logic gates (AND, OR, NOT, NAND, NOR, XOR), recognise their symbols, and write their truth tables. You also need to understand logic levels (a high voltage is logic 1, a low voltage is logic 0). Logic gates are the building blocks of every digital subsystem, and the truth table is how each one is defined and tested.
The answer
Logic levels
The AND, OR and NOT gates
The NAND, NOR and XOR gates
Truth tables
Examples in context
Logic gates are the physical building blocks of every digital part of the course. A security system might switch on a siren only when a door sensor and an armed switch are both active (an AND gate); a warning light might come on if either of two sensors trips (an OR gate). Combinational circuits such as adders and decoders are networks of these gates, and the same gates with feedback build the flip-flops and counters of the sequential module. Mastering the truth tables now makes Boolean algebra and circuit design straightforward.
Try this
Q1. State when a two-input AND gate outputs 1. [1 mark]
- Cue. Only when both inputs are 1.
Q2. Give the output of a two-input XOR gate for inputs . [1 mark]
- Cue. 1 (the inputs differ).
Q3. How many rows does the truth table of a three-input gate have? [1 mark]
- Cue. rows.
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 20194 marksComplete the truth table for a two-input NAND gate, and state in words when its output is low.Show worked answer →
Truth table (up to 3 marks): for inputs the AND outputs are , so the NAND (the inverse of AND) outputs .
In words (1 mark): the NAND output is low only when both inputs are high; for every other combination the output is high.
Markers reward the four correct output values () and the statement that the output is low only when both inputs are 1.
Eduqas 20223 marksExplain the difference between an OR gate and an XOR gate, using their outputs for the input combination where both inputs are 1.Show worked answer →
Difference (up to 2 marks): an OR gate outputs 1 when at least one input is 1 (including when both are 1); an XOR (exclusive-OR) gate outputs 1 only when the inputs are different, so it outputs 0 when they are the same.
Both inputs 1 (1 mark): for , the OR output is 1 but the XOR output is 0.
Markers reward the at-least-one versus exclusive distinction and the correct outputs for (OR gives 1, XOR gives 0).
Related dot points
- Boolean algebra: writing Boolean expressions for gates, the laws of Boolean algebra, De Morgan's laws, and simplifying an expression to use fewer gates.
An Eduqas GCSE Electronics answer on Boolean algebra: writing Boolean expressions using the AND, OR and NOT notation, the main laws of Boolean algebra, De Morgan's two laws, and simplifying an expression so a logic circuit uses fewer gates.
- 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.
- Binary numbers and adders: counting in binary, the half adder (sum and carry), the full adder with a carry in, and adding multi-bit numbers.
An Eduqas GCSE Electronics answer on binary arithmetic and adders: counting in binary and converting to decimal, the half adder built from XOR and AND giving sum and carry, the full adder that includes a carry in, and chaining full adders to add multi-bit binary numbers.
- Electronic systems and subsystems: the systems approach with input, process and output blocks, block diagrams and signal flow, and analogue versus digital signals.
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Sources & how we know this
- WJEC Eduqas GCSE (9-1) Electronics specification (C490) — WJEC Eduqas (2017)