2.1: Logical Operators & Truth Tables
Exam Board:
Eduqas / WJEC
Specification:
2020 +
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 four most common operators are:
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NOT
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AND
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OR
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XOR
What is a truth table?
A truth table is a visual way of displaying all possible outcomes of a logical operator.
The input and output values in a truth table must be a Boolean value - usually 0 or 1 but occasionally True or False.
NOT
A NOT logical operator will produce an output which is the opposite of the input.
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NOT is represented by a horizontal line.
Boolean Algebra Notation
written as
NOT A A
Truth Table
AND
An AND logical operator will output 1 only if both inputs are also 1.
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AND is represented by a full stop.
Boolean Algebra Notation
written as
A AND B A.B
Truth Table
OR
An OR logical operator will output 1 if either input is 1.
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OR is represented by a plus.
Boolean Algebra Notation
written as
A OR B A+B
Truth Table
XOR
An XOR (exclusive OR) logical operator will output 1 if the inputs are different and output 0 if the inputs are the same.
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XOR is represented by a circled plus.
Boolean Algebra Notation
written as
A XOR B A B
Truth Table
Multiple Operations
Exam questions will 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 column you need to use.
Simplification
You may be asked to use a truth table to simplify an expression.
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This is actually really easy. Once you've completed the truth table see if any columns match the final expression.
A+B and A+(A+B) both result in the same values, therefore:
A+(A+B) can be simplified as just A+B.
Questo's Questions
2.1 - Logical Operators:
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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.
