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## What is a logical operator?

Inside of each computer system are millions of transistors.

These are tiny switches that can either be turned on (represented in binary by the number 1) or turned off (represented by 0).

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Logical operators are symbols used to represent circuits of transistors within a computer. The three most common operators are:

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• NOT

• AND

• OR

## What is a truth table?

Truth tables are used to show all possible inputs and the associated output for each input.

The input and output values in a truth table must be a Boolean value - usually 0 or 1 but occasionally True or False.

## OR

A NOT logical operator will produce an output which is the opposite of the input.

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NOT is also known as Negation.

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The symbol for NOT is ¬

An AND logical operator will output 1 only if both inputs are also 1.

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AND is also known as Conjunction.

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The symbol for AND is

An OR logical operator will output 1 if either input is 1.

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OR is also known as Disjunction.

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The symbol for OR is

## Multiple Operators

Exam questions could ask you complete truth tables that use more than one logical operator.

Work out each column in turn from left to right and look carefully at which preceding column you need to use.

NOT B

A AND NOT B

A OR (A AND NOT B)

As binary is a base-2 number system, the number of rows required in a truth table will double with each new input in the expression in order to show the unique combinations of inputs. The examples above use just two inputs (A + B) so 4 rows are required.

e.g. A = 2 rows   /   A + B = 4 rows  /   A, B + C = 8 rows  /  A, B, C + D = 16 rows

## Logic Diagrams

You may be asked in an exam to draw a logic diagram when given a logical expression.

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Draw any NOT symbols or expressions in brackets first.

A logic diagram for C = ¬A ∧ B

A logic diagram for D = C ∨ (A ∧ B)

## Questo's Questions

4.1 - Boolean Logic:

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1. Copy and complete the following truth tables:

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1b. Simplify the expression in the second truth table.

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2a. A cinema uses a computer system to monitor how many seats have been allocated for upcoming movies. If both the premium seats and the standard seats are sold out then the system will display a message. State the type of logical operator in this example.

2b. For the more popular movies, the cinema's computer system will also display a message if either the premium seats or the standard seats have exclusively been sold out. However, it will not output a message when both have been sold out. State the type of logical operator in this example.

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3. Draw a logic diagram for C = (¬B v A) ∧ A.

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