NOR gate using NAND gates: four gates, live

A NOR gate takes four NAND gates: two NANDs with tied inputs invert A and B, a third NANDs those to make A OR B, and a fourth inverts that into NOR. Y is 1 only when A and B are both 0.

NOR is OR followed by NOT, so the recipe is the OR gate from three NAND gates plus one more NAND used as an inverter. The OR part is De Morgan's law: NAND(NOT A, NOT B) = NOT (NOT A AND NOT B) = A OR B. Equivalently, NOR = NOT A AND NOT B, which the circuit computes as the inverted inputs ANDed with NAND logic. Going the other way, a NAND gate from NOR gates also takes four, the dual of this circuit. The NAND universal gates page shows NOT, AND, OR and NOR from NANDs at once.

Live circuit: click the inputs to toggle them and watch the outputs update. It runs the real simulator, right here on the page.

Open this circuit in the lab →

Embed or cite this circuit

Free to embed on a course page, blog or worksheet: paste this code. The circuit stays live, and the small digiwleea badge links back here.

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To cite it: digiwleea, “NOR gate from NAND gates”, https://digiwleea.wleeaf.dev/tools/build/nor-from-nand/

What you need

2× NAND: inverters with tied inputs: NOT A and NOT B
1× NAND: O = NAND(NOT A, NOT B) = A OR B
1× NAND: Y = NAND(O, O) = A NOR B

Step by step

Place inputs A and B and a probe Y.
Invert A and B, each with a NAND gate whose inputs are tied together.
NAND the two inverted signals: that is A OR B.
Invert that with a fourth NAND gate and probe the result as Y.
Try all four rows: Y is 1 only for A = B = 0.

NOR from NAND truth table

A	B	NOT A	NOT B	A OR B	Y = A NOR B
0	0	1	1	0	1
0	1	1	0	1	0
1	0	0	1	1	0
1	1	0	0	1	0

All input rows are checked on the live circuit before the page is built.

You can also read the full theory in the lesson on the NAND gate. Prefer to build it yourself from scratch? Open the digiwleea lab and place the gates on the canvas, or start from the logic gate simulator.

More builds: Universal gates: NAND only, NOR only

OR gate from NAND gates OR gate from NOR gates AND gate from NAND gates AND gate from NOR gates NOT gate from a NOR gate XOR gate from NOR gates NOT gate from a NAND gate XNOR gate from NOR gates XNOR gate from NAND gates half adder from NAND gates XOR gate from NAND gates full adder from NAND gates

All 246 build guides, by topic

Each of these is one step from a transistor to a working CPU. Build every gate from CMOS transistors and work all the way up in the free digiwleea lab, with the free theory reference alongside.

Open the NOR gate from NAND gates in the lab →

Frequently asked

How many NAND gates are needed to make a NOR gate?

Four: two NANDs invert the inputs, a third NANDs them into A OR B, and a fourth inverts that into NOR.

How many NOR gates make a NAND gate?

Also four, by the same pattern with the roles swapped: invert both inputs with NORs, NOR them into AND, then invert.

Why is NAND a universal gate?

Because NAND alone can make NOT, AND and OR, and every Boolean function can be written with those three. NOR is universal for the same reason.