How this instrument works
NOR takes two inputs, A and B, and returns a single bit: NOT (A OR B). Compute OR first — true if either input is true — then flip that answer. The gate's whole behavior collapses to one sentence: NOR is 1 only when both A and B are 0, and 0 for the remaining three combinations, the mirror image of OR's own table.
The same result falls out of De Morgan's law without touching OR at all: A NOR B equals (NOT A) AND (NOT B). Negate each input on its own, then AND the two negations together, and both routes land on the identical bit every time. That equivalence is why a schematic drawn with a single NOR symbol and one drawn with two inverters feeding an AND gate describe the same circuit.
A property worth knowing: NOR is functionally complete on its own. Tie a NOR gate's two inputs together and it acts as an inverter; chain enough of these gates and every other Boolean function — AND, OR, XOR, anything — can be built with no other part. The Apollo Guidance Computer used exactly this trick: its logic boards held thousands of identical three-input NOR chips and nothing else, because one reliable part was cheaper to manufacture and test than several different ones.
- Type 0 or 1 into the A (0 or 1) field for the first input.
- Type 0 or 1 into the B (0 or 1) field for the second input.
- Read A NOR B: it shows 1 only when both fields hold 0, and 0 for every other pairing.
- Flip one input at a time and watch A NOR B switch to 0 the moment either field leaves zero.
Worked example — an alarm's all-clear signal
A security panel wires two motion sensors, A and B, into a NOR gate so the output reads 1 only when the room is genuinely empty. With neither sensor tripped, set A (0 or 1) to 0 and B (0 or 1) to 0. The formula computes OR first — 0 + 0 − (0 × 0) = 0 — then subtracts that from 1: A NOR B = 1 − 0 = 1. The panel's all-clear light turns on, matching the reference case 0 NOR 0 = 1 exactly.
Trip either sensor and the light goes out. Set A to 1 with B still 0: OR becomes 1 + 0 − 0 = 1, so A NOR B = 1 − 1 = 0. Set both sensors to 1 and the arithmetic reads 1 + 1 − 1 = 1 again, so A NOR B still returns 0. NOR only ever answers 1 at the single quiet corner of the truth table, the both-false row this example started from.
Questions
What does A NOR B actually compute?
NOR negates OR: work out A OR B first, then flip the bit. The result is 1 in exactly one row of the truth table, where both A and B equal 0, and 0 in the remaining three rows, where at least one input is 1.
How does NOR relate to the OR gate?
NOR is OR's exact opposite, one gate answering for the other. Wherever OR reports 1, the gate reports 0, and the single row where OR reports 0 — both inputs false — is the only row where NOR reports 1. The two share one truth table, inverted top to bottom.
Why is NOR called a universal gate?
Because every other Boolean function — NOT, AND, OR, XOR, and beyond — can be built from these gates alone, with no other component. Tie one gate's two inputs together and it becomes an inverter; combine inverted and un-inverted versions and the rest follow. Entire early computers, including the Apollo Guidance Computer, were built from nothing but repeated NOR gates.
What mistake do people usually make with NOR?
Assuming the gate's lone 1 sits at both-inputs-true, the way AND's lone distinctive row does. It doesn't: NOR's only 1 sits at both-inputs-false, the mirror image of AND's pattern rather than a copy of it. Confusing the two rows gives the wrong answer in three of the four cases.
How does De Morgan's law explain NOR?
De Morgan's law states that negating an OR equals ANDing the two negated inputs: A NOR B = (NOT A) AND (NOT B). Both formulas describe the identical function, so a circuit drawn with one such gate and a circuit drawn with two inverters feeding an AND gate behave identically for every input pair.
Is NOR the same thing as NAND?
No — they are near-mirror opposites with different single-row exceptions. NAND is 0 only when both inputs are 1, and 1 everywhere else; NOR is 1 only when both inputs are 0, and 0 everywhere else. They agree at 0,0 and 1,1 but disagree at 0,1 and 1,0, where NAND reads 1 and NOR reads 0.