Computer Science • Logic Gates & Circuits

Circuit Dash

Standard

AND, OR and NOT · up to 3 inputs and 2 levels · gate names and the Boolean expression shown

  • Each round shows a circuit and the value on each input (A, B, C, D) on the left. Call the output Y: Y = 0 or Y = 1, or press 0 / 1.
  • You start with 60 seconds. A right answer adds time; a wrong one takes some away.
  • Every three right answers the circuits get bigger, and bigger circuits score more.
  • New to logic gates? The Explanation has every gate, its truth table, and how to work a circuit out.
Your best in this mode: 0

Circuit Dash — Explanation

The game. Each round shows a logic circuit and the value on each input. Follow the signals through the gates and call the output, Y: 0 or 1, by clicking or pressing 0 or 1. You start with 60 seconds; a right answer adds time and a wrong one takes some away. After each answer every wire shows its value, so you can see how the output was reached. Every three right answers the circuits get bigger, and bigger circuits score more: 10 × inputs × levels of gates (a NOT gate doesn't count as a level).

The gates

Reading a circuit diagram

Boolean notation

A · B or ABA AND B
A + BA OR B
ANOT A (a bar over the top)
A ⊕ BA XOR B: 1 when the inputs differ
A · BA NAND B
A + BA NOR B

NOT is worked out first, then AND, then OR, just as multiplication comes before addition. Brackets change the order.

Working out a circuit

  1. Write each input's value on its wire.Where a wire splits (a dot), every branch carries the same value.
  2. Work through the gates from left to right.A gate can only be worked out once all its inputs are known.
  3. Write each gate's output on the wire leaving it.A NOT gate (a triangle and circle) simply flips 0 ↔ 1.
  4. The value reaching Y is the answer.Example: Y = A·B + A̅·C with A = 1, B = 0, C = 1 → A·B = 0, A̅·C = 0, so Y = 0.

Objective: work out the output of a logic circuit of up to three levels of gates for any combination of inputs, recognise the AND, OR, NOT, NAND, NOR and XOR symbols and their truth tables, and link a circuit diagram to its Boolean expression.

Where this fits

  • AQA: AQA A Level Computer Science (7517)
  • Cambridge: Cambridge IGCSE Computer Science (0478); Cambridge A Level Computer Science (9618); Cambridge AS Level Computer Science (9618)
  • IB: IB Computer Science HL; IB Computer Science SL
  • Pearson Edexcel International: Edexcel International GCSE Computer Science (4CP0) Goes beyond Edexcel International GCSE Computer Science (4CP0): 4CP0 has AND, OR and NOT logic statements only; gate symbols, circuits and NAND, NOR and XOR go beyond it.
  • USDP: USDP Computer Science

Circuit Dash — Key Terms

Key concepts in English, with te reo Māori, Chinese (Simplified) and Korean.

EnglishTe reo Māori中文（简体）한국어What it means on this page
Logic gateno attested term逻辑门논리 게이트A component that takes one or two binary inputs and gives one binary output according to a fixed rule.
AND gateno attested term与门AND 게이트Output 1 only when both inputs are 1. Written A · B, or AB.
OR gateno attested term或门OR 게이트Output 1 when at least one input is 1. Written A + B.
NOT gate (inverter)no attested term非门NOT 게이트One input; the output is the opposite. Written with a bar: A̅. It doesn't count as a level here.
NAND gateno attested term与非门NAND 게이트NOT AND: output 0 only when both inputs are 1.
NOR gateno attested term或非门NOR 게이트NOT OR: output 1 only when both inputs are 0.
XOR gate (exclusive OR)no attested term异或门XOR 게이트Output 1 when the two inputs are different. Written A ⊕ B.
Inputtāuru输入입력A value fed into the circuit — A, B, C or D on the left.
Outputhuaputa输出출력The value the circuit produces — Y on the right.
Truth tableno attested term真值表진리표A table listing the output for every possible combination of inputs.
Boolean expressionkīanga Pūreana布尔表达式불 표현식The circuit written in symbols, e.g. Y = A·B + A̅·C.
Expressionkīanga表达式표현식A combination of values and operators that works out to a single value.
Logical operationmahi arorau逻辑运算논리 연산An operation such as AND, OR or NOT carried out on binary values.
BooleanPūreana布尔불Having only two possible values: 1 (true) or 0 (false).
Level (of gates)no attested term逻辑层级게이트 단계How many gates a signal passes through on the longest path to Y, not counting NOT gates.
Binarytāhūrua二进制이진법Base 2 — every wire here carries a 0 or a 1.
Bitmoka位비트A single binary digit: the value on one wire.

On the te reo Māori column. Terms marked as gaps have no attested equivalent in the sources checked — Karaitiana Taiuru's Dictionary of Māori Computer and Social Media Terms, Paekupu, the Reserve Bank's te reo financial glossary, NZQA and Te Aka. No coinage is printed as though it were established; where a class needs one, commission it from Te Taura Whiri i te Reo Māori and credit the translator. Te reo Māori is not italicised and takes no plural "s".