Flashcards · 0478 · Topic 10

Boolean logic flashcards

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When is the output of a NOT, AND and OR gate 1?: NOT: when the input is 0 (it inverts). AND: only when both inputs are 1. OR: when at least one input is 1.
When is the output of a NAND, NOR and XOR gate 1?: NAND: unless both inputs are 1. NOR: only when both inputs are 0. XOR: only when the inputs are different.
Truth table for XOR (A, B → X): 0, 0 → 0 0, 1 → 1 1, 0 → 1 1, 1 → 0
Truth table for NAND (A, B → X): 0, 0 → 1 0, 1 → 1 1, 0 → 1 1, 1 → 0
How many rows does a truth table have?: 2ⁿ rows for n inputs: 4 rows for two inputs and 8 rows for three. List them in binary counting order (000, 001, 010 ...).
OR vs XOR: OR gives 1 when either or both inputs are 1. XOR gives 1 only when exactly one input is 1.
Is A NAND B the same as (NOT A) AND (NOT B)?: No. A NAND B is NOT (A AND B), which is 1 unless both inputs are 1. (NOT A) AND (NOT B) is 1 only when both are 0, which is NOR.
How do you write a logic expression from a problem statement?: Give each condition a letter, then join them with AND (both), OR (either) and NOT (not / unless), using brackets. E.g. heater on when cold and window not open: H = C AND (NOT W).
How do you complete a truth table for a circuit with several gates?: Add a working column for the output of each gate and fill them left to right through the circuit, then the final output. Working columns can earn marks even if the final column is wrong.