NOR gate truth table
The NOR gate outputs 1 only when both inputs are 0, and 0 otherwise. It is the inverse of OR. Here is its full truth table, the boolean expression, and how it is actually built.
| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
Boolean expression: Y = (A + B)̅. A 1 in the table means a high voltage (logic true) and a 0 means low (false). Read each row as: for these inputs, the output Y is this value.
What the NOR gate does
NOR is the other universal gate: like NAND, any logic function can be built from NOR gates alone. It is also four transistors in CMOS, with the pull-up and pull-down networks swapped relative to NAND.
Build it yourself
Reading a table is one thing; watching the signals flow is another. Open the logic gate simulator and wire a NOR gate up from transistors, or read the full lesson on how this gate is designed. You can also generate the table for any expression with the truth table generator.
Other gates:
The NOR gate is one small step toward a working CPU. Build every gate from CMOS transistors and work up to an 8-bit processor in the free digiwleea lab and course.
Open the gate simulator →Frequently asked
What is the truth table of a NOR gate?
The NOR gate outputs 1 only when both inputs are 0, and 0 otherwise. It is the inverse of OR. For inputs (A,B) the outputs are 0,0→1 0,1→0 1,0→0 1,1→0.
What is the boolean expression for NOR?
The NOR gate is written Y = NOT (A OR B) (symbolically Y = (A + B)).
How many transistors does a NOR gate take?
A standard CMOS NOR gate uses about 4 transistors. In digiwleea you build it from those transistors and the simulator verifies it against this exact truth table.