Exam code:J277
Combining Boolean Operators
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Boolean operators can be combined to produce more complex expressions
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The combination of two or more Boolean operators forms a logic expression
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Brackets are used to clarify the order of operations
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A logic diagram is a visual representation of combinations of Boolean operators within a logic circuit
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An example would be Q = NOT(A OR B)
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In the diagram above, the inputs are represented by A and B
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P is the output of the OR gate on the left and becomes the input of the NOT gate
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Q is the final output of the logic circuit
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This is a logic diagram for the Boolean expression Q = NOT(A OR B)
Examiner Tips and Tricks
You may be asked to draw a logic circuit from a logic statement or a Boolean expression OR write the logical expression that is expressed in the logic diagram
Logic circuits will be limited to a maximum of three inputs and one output
Example of combining Boolean operators
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P = (A OR B) AND NOT C
Apply Logical Operators in Truth Tables
What is a truth table?
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A truth table is a tool used in logic and computer science to visualise the results of Boolean expressions
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They represent all possible inputs and the associated outputs for a given Boolean expression
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To create a truth table for the expression P = (A AND B) AND NOT C
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Calculate the numbers of rows needed (2number of inputs)
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In this example there are 3 inputs (A, B, C) so a total of 8 rows are needed (23)
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To not miss any combination of inputs, start with 000 and count up in 3-bit binary (0-7)
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|
A |
B |
C |
|
0 |
0 |
0 |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
0 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
|
1 |
1 |
1 |
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Add a new column to show the results of the brackets first (A AND B)
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Add a new column to show the results of NOT C
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The last column shows the result of the Boolean expression by comparing (A AND B) AND NOT C
Examiner Tips and Tricks
It is possible to create a truth table when combining expressions that show only the inputs and the final outputs.
The inclusion of the extra columns supports the process but can be skipped if you feel able to do those in your head as you go.
Worked Example
Complete the truth table for the following logic diagram [4]
Responses