Inside every processor, tiny logic gates make decisions using just 1 (true) and 0 (false). This mini-lesson covers the six gates — AND, OR, NOT, NAND, NOR, XOR — their truth tables, and how to read and build logic circuits and Boolean expressions.
Work through each screen, answer the questions as you go, and collect ⭐ stars. Double-check every truth-table row! Press Start when ready.
Gates · AND, OR, NOT
AND, OR and NOT
AND — output is 1 only when BOTH inputs are 1.
OR — output is 1 when AT LEAST ONE input is 1.
NOT — has one input; it inverts it (0→1, 1→0).
Learn these three first — the others are built from them.Quick check
AND gate output
?An AND gate has inputs A = 1 and B = 0. What is the output?
Gates · NAND, NOR, XOR
NAND, NOR and XOR
NAND = NOT AND — the opposite of AND. Output is 0 only when both inputs are 1, otherwise 1.
NOR = NOT OR — the opposite of OR. Output is 1 only when both inputs are 0.
XOR (exclusive OR) — output is 1 only when the two inputs are DIFFERENT.
NAND and NOR are just AND and OR with the output flipped.Quick check
XOR gate output
?An XOR gate has inputs A = 1 and B = 1. What is the output?
Quick check
NOR gate output
?For which single set of inputs does a NOR gate output 1?
Match it
Match each rule to its gate
Tap a rule on the left, then the gate on the right.
Rule
Gate
Logic circuits & expressions
Circuits & Boolean expressions
Gates are joined into logic circuits. We can write the same logic as a Boolean expression using the operators AND, OR, NOT. Work from the inputs, through each gate, to the output X.
This circuit gives the Boolean expression X = (A AND B) OR (NOT C).
Worked example — complete the truth table for X = (A AND B) OR (NOT C)
If A=1, B=1, C=1: (1 AND 1)=1, so X = 1 OR (NOT 1) = 1 OR 0 = 1.
If A=0, B=1, C=1: (0 AND 1)=0, X = 0 OR (NOT 1) = 0 OR 0 = 0.
Quick check
Read the circuit
?For X = (A AND B) OR (NOT C), what is X when A = 0, B = 1, C = 0?
Quick check
Another expression
?For X = A XOR (B AND C), what is X when A = 1, B = 1, C = 1?
Quick check
Naming a gate
?A gate outputs 1 for the input pairs (0,0), (0,1) and (1,0), but outputs 0 for (1,1). Which gate is it?
Recap
The big ideas to know
AND = 1 only when both inputs are 1
OR = 1 when at least one input is 1
NOT = inverts a single input
NAND = NOT AND (0 only when both are 1) · NOR = NOT OR (1 only when both are 0)
XOR = 1 only when the inputs are different
Circuits & expressions: trace input → gate → output; write as (A AND B) OR (NOT C) etc.
You’ve covered the whole of Boolean logic. Press Finish to see your score.
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