Explain how a logic diagram is turned into a Boolean expression.

Each gate is written as an expression of its inputs, working from the inputs towards the output. Brackets group the part of the expression each gate works on.

Inputs A and B feed an OR gate, and that gate's output feeds an AND gate with input C. What is the expression for the output P?

The expression is P = (A OR B) AND C. The brackets show that the OR gate is worked out before the AND gate.

How do NOT (A AND B) and (NOT A) AND B differ?

In NOT (A AND B), the AND gate is worked out first and its output is inverted. In (NOT A) AND B, only A is inverted before it enters the AND gate.

What is the output of NOT (A OR B) when A = 0 and B = 0?

The output is 1. A OR B gives 0 because neither input is 1, and NOT 0 gives 1.

OCR GCSE Computer Science J277

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Boolean Logic

Topic overview Logic gates and truth tables Combining gates in logic diagrams

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Boolean Logic

Combining gates in logic diagrams

4 things to know
J277/02

Overview

Turning logic diagrams into Boolean expressions and back, worked outputs for combined gates, truth tables for expressions, and designing circuits for alarms and heaters.

What you need to know

Answer each one before you reveal it.

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Key term

Which gates are needed to build the circuit P = (NOT A) OR (B AND C)?

Key term

What is the output of NOT ((A OR B) AND C) when A = 0, B = 1 and C = 1?

Numbers

In the truth table for P = (A AND B) OR C, how many of the eight rows give P = 1?

Key term

What is a logic diagram?

Questions from this subtopic

Each one with the model answer underneath.

1
What is a logic diagram?
Model answer
A logic diagram shows gate symbols joined by lines to form a circuit. The inputs enter on the left and the final output leaves on the right.
2
Explain how a logic diagram is turned into a Boolean expression.
Model answer
Each gate is written as an expression of its inputs, working from the inputs towards the output. Brackets group the part of the expression each gate works on.
3
Inputs A and B feed an OR gate, and that gate's output feeds an AND gate with input C. What is the expression for the output P?
Model answer
The expression is P = (A OR B) AND C. The brackets show that the OR gate is worked out before the AND gate.
4
Which gates are needed to build the circuit P = (NOT A) OR (B AND C)?
Model answer
Three gates are needed. A NOT gate inverts A and an AND gate combines B and C. An OR gate then joins the two results.
5
How do NOT (A AND B) and (NOT A) AND B differ?
Model answer
In NOT (A AND B), the AND gate is worked out first and its output is inverted. In (NOT A) AND B, only A is inverted before it enters the AND gate.
6
What is the output of NOT (A OR B) when A = 0 and B = 0?
Model answer
The output is 1. A OR B gives 0 because neither input is 1, and NOT 0 gives 1.

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