Knowledge Organiser: Truth Tables and Combined Logic Circuits
Key Terms
- Truth table: A table showing all possible input combinations and their corresponding outputs
- Combined logic circuit: A circuit using multiple gates connected together
- Intermediate column: A column in a truth table showing the output of a gate within a larger circuit
- Boolean order of operations: Brackets → NOT → AND → OR (same concept as BIDMAS)
Must-Know Facts
- Number of rows in a truth table = 2ⁿ where n is the number of inputs
- 1 input = 2 rows; 2 inputs = 4 rows; 3 inputs = 8 rows
- Always show intermediate columns — you earn method marks even if the final answer is wrong
- Order of operations: Brackets first, then NOT, then AND, then OR (lowest priority)
- Work column by column (complete all rows for one gate before moving to the next)
- Input columns follow a binary counting pattern: rightmost alternates 0,1,0,1…
Key Concepts
- To evaluate NOT(A) AND B: Step 1 calculate NOT(A); Step 2 apply AND with B
- To evaluate (A AND B) OR C: Step 1 calculate A AND B; Step 2 apply OR with C
- Label each intermediate column clearly (e.g. "NOT A", "A AND B")
- Double-check row count before submitting — wrong row count loses all marks
Common Mistakes
- Wrong number of rows: Always use 2ⁿ rows where n is the number of inputs — 2 inputs = 4 rows, 3 inputs = 8 rows; a missing row means marks are lost for every output in that row
- Filling input columns in wrong order: The rightmost input column alternates 0,1,0,1 — the next column alternates 0,0,1,1,0,0,1,1 — this binary counting pattern must be followed exactly
- Applying operations in the wrong order: Evaluate brackets first, then NOT, then AND, then OR — skipping intermediate columns makes errors very hard to spot
- Confusing AND and OR outputs: AND only outputs 1 when BOTH inputs are 1; OR outputs 1 when ANY input is 1 — mixing these up is the most common single error in truth table questions