You can derive a Boolean expression directly from a truth table using the Sum of Products (SOP) method:
Step 1: Find all rows where the output = 1
Step 2: For EACH of those rows, write an AND expression:
- If an input is 1, write it as-is (A)
- If an input is 0, write it with NOT (NOT(A))
Step 3: OR all these AND expressions together
Given: Output is 1 when:
- Row 1: A=0, B=1 → Output=1
- Row 2: A=1, B=1 → Output=1
Step 1: Identify rows with output 1 ✓
Step 2: Write AND expressions for each row:
- Row 1 (A=0, B=1): NOT(A) AND B
- Row 2 (A=1, B=1): A AND B
Step 3: OR them together:
(NOT(A) AND B) OR (A AND B)
Simplified: This actually simplifies to just B (because B is 1 in both cases, regardless of A)
This key facts covers Writing Expressions from Truth Tables within Boolean Expressions for GCSE Computer Science. Revise Boolean Expressions in 3.4 Computer Systems for GCSE Computer Science with 17 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 7 of 12 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Boolean Expressions
Which Boolean operator produces an output of 1 only when BOTH inputs are 1?
State De Morgan's first law and give an example to illustrate it.