NOR gate

OR with the answer flipped — on only when everything is off. A plain-English guide to logic gates from TorchAnvil.

A NOR gate is an OR with the answer inverted. Its output is high only when every input is low. Any input going high pulls it down.

How to read it

A	B	A + B	A NOR B
0	0	0	1
0	1	1	0
1	0	1	0
1	1	1	0

One 1, three 0s. NOR fires only in the all-quiet case, which makes it the natural gate for "nothing is happening" — no faults raised, no buttons pressed, no requests pending.

Why it matters

Two reasons, and the second is the bigger one.

First, NOR is functionally complete, exactly like NAND. Everything can be built from it:

• NOT A = A NOR A
• A OR B = (A NOR B) NOR (A NOR B)
• A AND B = (A NOR A) NOR (B NOR B)

Second — and this is why NOR earns its place in every curriculum — two NOR gates cross-coupled make a memory cell. Feed each gate's output back into the other's input, leave one input free on each, and you have an SR latch: a circuit that remembers.

Pulse the Set input and the output goes high and stays high after the pulse ends. Pulse Reset and it goes low and stays low. That's one bit of storage, built from two gates and a pair of wires. Every register, every cache line, every byte of static RAM descends from this arrangement.

A worked example: the SR latch

Wire it up:

• NOR gate 1: inputs are Reset and the output of gate 2. Call its output Q.
• NOR gate 2: inputs are Set and Q. Call its output Q̄.

Now reason through it. Set is 1, Reset is 0. Gate 2 has a high input, so Q̄ goes 0. Gate 1 now sees Reset=0 and Q̄=0 — all inputs low — so Q goes

1. Drop Set back to 0: gate 2 still sees Q=1, so Q̄ stays 0, so Q stays 1. The circuit is holding a value with no input driving it.

That feedback loop is the whole trick. Combinational logic answers questions about now; the moment you route an output back to an input, the circuit gains a past.

One combination is forbidden: Set and Reset both high forces Q and Q̄ both low, which contradicts their names, and when you release them the result depends on which input falls first. Real designs use a gated latch or a D flip-flop to make that state unreachable.

How it differs from NAND

Both invert, both are universal, and they are duals of each other:

A	B	NOR	NAND
0	0	1	1
0	1	0	1
1	0	0	1
1	1	0	0

NOR is high only when all inputs are low. NAND is low only when all inputs are high. Each is the other read upside down. De Morgan again:

• NOT(A + B) = NOT A · NOT B

A NOR is an AND of inverted inputs. That's the identity you'll use most often when simplifying real circuits.

In redstone

NOR is the gate redstone hands you almost free, and it's the reason the torch matters so much.

Take a block. Run two input dust lines into it. Put a torch on the side. If either input powers the block, the torch goes out. Only when both are off does the torch stay lit. That's a two-input NOR in one torch and one block, costing a single tick.

Because OR is free — merged dust — and inversion is one torch, NOR is the cheapest non-trivial gate in Minecraft. Widening it is free too: run eight lines into the same block and one torch gives you an 8-input NOR.

This is why redstone builds look the way they do. In silicon NAND is the cheap primitive; in redstone it's NOR, and efficient designs are usually the ones that lean into it.

A historical footnote

The Apollo Guidance Computer — the machine that ran the descent to the lunar surface in 1969 — was built almost entirely from NOR gates. Around five thousand of them, three-input, packaged two to a chip, and virtually nothing else.

That wasn't nostalgia for elegance. It was manufacturing discipline: one part number to qualify, one failure mode to characterise, one thing to test. Functional completeness meant the whole computer could be expressed in that single gate, and the reliability argument won.

It's a useful thing to remember when you're staring at a palette of eight gate types and wondering which is "real". Any one of NAND or NOR is sufficient; the rest are conveniences.

Gotchas

• Not associative, same as NAND. (A NOR B) NOR C ≠ A NOR (B NOR C). Build wide NORs as a wide OR with one inversion at the end.
• The forbidden state is real. In an SR latch, asserting Set and Reset together produces behaviour that depends on release order. Don't design around it; design it out.
• A NOR whose inputs are tied together is just an inverter, which is handy but easy to create by accident when wiring quickly.

Try it

The demo on the right is two levers into a NOR into a lamp. The lamp is on only when both levers are down.

Then build the SR latch: two NORs, cross-coupled, two levers for Set and Reset, a lamp on Q. Pulse Set, then let go. The lamp stays lit — and you've built your first memory.

Frequently asked questions

What is a NOR gate?

A NOR gate is an OR gate with its output inverted. It outputs high only when every input is low; any input going high pulls the output down.

Why are NOR gates used to build memory?

Two NOR gates cross-coupled — each output feeding the other's input — form an SR latch. Pulsing Set drives the output high and it stays high after the pulse ends, storing one bit. Every static RAM cell descends from this arrangement.

How do you build a NOR gate in Minecraft redstone?

Run both input lines into the same block and place a redstone torch on its side. If either input powers the block the torch goes out, so the torch is lit only when both inputs are off. One torch, one tick.

What is the difference between NOR and NAND?

NOR is high only when all inputs are low; NAND is low only when all inputs are high. They are duals, and both are functionally complete, so either one alone can build every other gate.

What is the forbidden state of an SR latch?

Asserting Set and Reset at the same time. It forces both outputs low, contradicting the fact that they should be opposites, and the value you end up with depends on which input is released first.