Logic Expressions (Cambridge International IGCSE Computer Science)
Exam board Cambridge International · IGCSEUpdated 2024-10-11
Spec point — "(c) Write a logic expression from a: (i) problem statement (ii) logic circuit (iii) truth table"
Logic Expressions
- A logic expression is a way of expressing a logic gate or logic circuit as an equation
- The output appears on the left of the equals sign with the inputs and logic gates on the right
| Gate | Symbol | Truth Table | Logic Expression |
|---|---|---|---|
| NOT |  | | A | Z | |---|---| | 0 | 1 | | 1 | 0 | | Z = NOT A |
| AND |  | | A | B | Z | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | | Z = A AND B |
| OR |  | | A | B | Z | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 | | Z = A OR B |
| NAND |  | | A | B | Z | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | | Z = A NAND B |
| NOR |  | | A | B | Z | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 0 | | Z = A NOR B |
| XOR |  | | A | B | Z | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | | Z = A XOR B |
- Logic circuits containing multiple gates can also be expressed as logic expressions/statements
An example logic circuit containing two inputs
- The logic circuit above can be expressed as the logic expression Q= NOT(A OR B)
An example logic circuit containing two inputs
- The logic circuit above can be expressed as the logic expression Q= (NOT A) AND B
An example logic circuit containing three inputs
- The logic circuit above can be expressed as the logic expression P = ((NOT A) OR B) NAND C
An example logic circuit containing three inputs
- This logic circuit above can be expressed as X = NOT (A NAND B) OR (B NOR C)
Exam Hint
- You may be required to write a logic expression/statement from a truth table or a logic circuit. You may also have to do the opposite - draw a logic circuit and complete a truth table for a logic expression
Worked Example Consider the logic statement: X = (((A AND B) OR (C AND NOT B)) XOR NOT C)
a. Draw a logic circuit to represent the given logic statement. [6]
Final answer: Answer
One mark per correct logic gate, with the correct input
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