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Truth tables with three inputs
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Real systems often depend on three conditions at once. A truth table with three inputs shows every possible situation.
Eight rows
Each input can be 0 or 1, so 3 inputs give 2 × 2 × 2 = 8 combinations.
List them in binary order: 000, 001, 010, 011, 100, 101, 110, 111.
List them in binary order: 000, 001, 010, 011, 100, 101, 110, 111.
Work in stages
Add a column for each part of the expression. Here P = (A AND B) OR C.
From a problem to logic
Pick out the conditions and join them with AND, OR, NOT.
"The alarm (P) sounds if the door is open (A) AND the system is on (B), OR the panic button (C) is pressed."
P = (A AND B) OR C
"The alarm (P) sounds if the door is open (A) AND the system is on (B), OR the panic button (C) is pressed."
P = (A AND B) OR C
Find P = A AND NOT B when A = 1, B = 0.
- NOT B = NOT 0 = 1
- A AND 1 = 1 AND 1 = 1
Answer: P = 1
Three inputs give 8 rows. Work through the expression in stages with extra columns. Turn word problems into logic by finding the conditions and the joining words.
The interactive lesson includes the diagrams for this topic.
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