Computer Science · Boolean logic. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A truth table lists every possible combination of inputs to a logic circuit and the output for each one. With 2 inputs there are 4 rows. With 3 inputs there are 8 rows. The rows are written in binary counting order, from 000 up to 111.
To complete a table from an expression or a circuit, do not jump straight to the final output. Work out the output of each gate or bracket first, as an extra working column, and then combine those results.
For a problem statement, first turn the words into an expression, or mark the rows where the stated conditions are met, taking care with what 1 and 0 mean for each input.
Students try to do a whole row in their head and lose a NOT on the way. Write the intermediate values for each row, and use XOR = 0 when both inputs are 1.
Answer: 3 rows
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