Constructing Truth Tables

Truth tables are a systematic way to enumerate every possible combination of inputs and determine the resulting output for a Boolean expression or logic circuit. They are an essential tool for analysing, verifying, and comparing logic circuits and Boolean expressions in OCR H446.

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Why Truth Tables Matter

Truth tables allow you to:

• Verify that a Boolean expression is correct
• Compare two expressions to see if they are logically equivalent
• Debug a logic circuit by checking expected outputs against actual outputs
• Prove Boolean algebra identities

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How Many Rows?

The number of rows in a truth table depends on the number of input variables:

Variables	Rows (2^n)
1	2
2	4
3	8
4	16
5	32

Key Term: For n input variables, a truth table has 2^n rows. Each row represents a unique combination of 0s and 1s.

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Standard Input Ordering

Inputs should be listed in a standard binary counting pattern. For three variables A, B, C: