AND gate using NOR gates: three gates, live
An AND gate takes three NOR gates: two NORs with their inputs tied together invert A and B, and a third NORs the inverted inputs, so Y = NOR(NOT A, NOT B) = A AND B. The live circuit below shows all four rows.
This is De Morgan's law again: NOT (NOT A OR NOT B) = A AND B. A NOR gate fed the inverted inputs computes the left side, and a NOR with both inputs joined is an inverter, because NOR(A, A) = NOT A. That one-gate inverter is also the answer to "NOT gate using NOR". It is the exact mirror of the OR gate from three NAND gates: swap NAND for NOR and OR for AND. Because NOR alone can make NOT, AND and OR, it is a universal gate; the NOR universal gates page builds them side by side, and the same AND sits inside the half adder from NOR gates as its carry.
Open this circuit in the lab →
What you need
- 2× NOR: inverters, each with both inputs tied: NOT A and NOT B
- 1× NOR: Y = NOR(NOT A, NOT B) = A AND B
Step by step
- Place inputs
AandBand a probeY. - Feed A into both inputs of a NOR gate: its output is NOT A. Do the same for B.
- NOR the two inverted signals together and probe the result as
Y. - Try all four rows: Y is 1 only when A and B are both 1, which is AND.
AND from NOR truth table
| A | B | NOT A | NOT B | Y = A AND B |
|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 |
The last NOR outputs 1 only when both of its inputs are 0, that is when A and B are both 1. All four rows are checked on the live circuit before the page is built.
You can also read the full theory in the lesson on NOR as a universal 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
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 AND gate from NOR gates in the lab →Frequently asked
How many NOR gates are needed to make an AND gate?
Three: two NOR gates used as inverters (inputs tied together) and one NOR that combines the inverted inputs. NOR(NOT A, NOT B) = A AND B by De Morgan's law.
How do you make a NOT gate using a NOR gate?
Tie both inputs of the NOR gate together, or tie one input to 0. NOR(A, A) = NOT A, and NOR(A, 0) = NOT A as well.
How do you make an OR gate from NOR gates?
Use two: a NOR followed by a NOR wired as an inverter. NOT (NOR(A, B)) = A OR B.
How many NOR gates make a NAND gate?
Four: the three-NOR AND gate followed by one more NOR wired as an inverter.