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OCR H446 1.4.3 Circuits, expressions and truth tables

Part 3 of 11 · H446 1.4.3 · Boolean algebra

Moving in any direction between scenario, expression, circuit and truth table is the central demand of OCR H446 1.4.3, and it is where bracket errors surface. This worksheet drills all four representations together, including reading an expression back off a circuit by starting at the final gate.

Students will:

  • complete a full truth table using systematic input ordering
  • write an expression from a circuit by working backwards from the final gate
  • draw a labelled circuit from a given expression while preserving grouping
  • match a Boolean expression to the circuit that produces it
  • work out how many rows a complete truth table needs for a defined set of variables

Inside: 6 explanation cells, 2 multiple-choice questions, 3 fill-in-the-blanks cells and 2 written answers. 28 marks, about 45 to 55 minutes.

Series: H446 1.4.3 · Boolean algebra, part 3 of 11.

Shared by Coding PathwayVerified teacher

  • 13 cells
  • About 45 minutes
  • CC BY-SA 4.0
  • Shared 31 Aug 2026
  • Updated 3 Sept 2026

Preview

The whole resource, exactly as a class sees it. Answers and marking are held back.

Circuits, expressions and truth tables

OCR expects you to move in every direction between a scenario, Boolean expression, logic circuit and truth table. They are different representations of the same logic.

You should already know: gate symbols and intermediate signals.

Worked model: one circuit, three written stages

Circuit for P equals open bracket A OR B close bracket AND NOT CABCDEP

The circuit gives P = (A ∨ B) ∧ ¬C. Work from inputs towards the output. Brackets record the fact that A ∨ B happens before the final AND.

A three-input truth table has 2³ = 8 rows. List inputs systematically from 000 to 111, add intermediate columns, then calculate the final output.

Fill in the blanks6 marks
Complete the first half of the truth table. The input state is shown once; enter each intermediate or final value on its own narrow-screen-safe line. ABC=000 - D = A ∨ B: row 1 D - E = ¬C: row 1 E - P = D ∧ E: row 1 P ABC=001 - D = A ∨ B: row 2 D - E = ¬C: row 2 E - P = D ∧ E: row 2 P ABC=010 - D = A ∨ B: row 3 D - E = ¬C: row 3 E - P = D ∧ E: row 3 P ABC=011 - D = A ∨ B: row 4 D - E = ¬C: row 4 E - P = D ∧ E: row 4 P
Fill in the blanks6 marks
Now complete the second half without changing the method. ABC=100 - D = A ∨ B: row 5 D - E = ¬C: row 5 E - P = D ∧ E: row 5 P ABC=101 - D = A ∨ B: row 6 D - E = ¬C: row 6 E - P = D ∧ E: row 6 P ABC=110 - D = A ∨ B: row 7 D - E = ¬C: row 7 E - P = D ∧ E: row 7 P ABC=111 - D = A ∨ B: row 8 D - E = ¬C: row 8 E - P = D ∧ E: row 8 P
Multiple choice1 mark

Which expression matches the model circuit?

  • AA ∨ (B ∧ ¬C)
  • B¬((A ∨ B) ∧ C)
  • C(A ∨ B) ∧ ¬C
  • D(A ∧ B) ∨ ¬C
Multiple choice1 mark

For P=(A ∨ B) ∧ ¬C, which input state makes P=1?

  • AA=0, B=0, C=0
  • BA=1, B=0, C=1
  • CA=1, B=1, C=1
  • DA=0, B=1, C=0

Reverse translation: start at the final gate

When writing an expression from a circuit, begin with the final gate. Write a placeholder for each of its inputs, then replace each placeholder with the expression produced by the earlier gate. This preserves grouping.

When drawing a circuit from an expression, do the reverse: evaluate the innermost bracket or negation first and connect its output to the next operator.

Written answer4 marks

On paper, draw a logic circuit for R = ¬(A ∧ B) ∨ C. Label every input and the output R.

Build A ∧ B, invert that whole result, then combine it with C using OR.

Students type their answer here.

Written answer6 marks

A greenhouse fan runs when the temperature is high and either a window is closed or rain is detected. Define variables and give the expression. Then state the number of rows needed in its complete truth table.

There are three independent input variables.

Students type their answer here.

Examination lens

An OCR-style question may award separate marks for sub-expressions and the correct final connection. Show brackets clearly. In a truth table, systematic input ordering prevents missing or repeated combinations.

Closed-book checkpoint

Complete these fresh retrieval statements. Checking is held for teacher review.

Fill in the blanks4 marks
A truth table with n independent inputs needs entry 1 rows. Naming values between gates creates entry 2 columns. When reading a circuit, begin at the inputs but use the entry 3 gate to organise the final expression. Brackets preserve the entry 4 in which gate results are combined.

Review your responses

Check every response against its command word and the supplied constraints. Strengthen unsupported answers with accurate method, mechanism, state or contextual consequence before submitting.