NOR Gate Calculator

Calculate NOR logic gate output: NOT(A OR B). Supports single-bit and multi-bit operations.

NOR Gate Input

Click to toggle between 0 and 1:

Input A:
Input B:

NOR Truth Table

ABA OR BNOR (Output)
0001
0110
1010
1110

Result

NOR Output
1
NOT(A OR B)
Input A0
Input B0
A OR B0
NOT(A OR B)1
Decimal Result1

Step-by-Step Solution

NOR(0, 0) = NOT(0 OR 0) = NOT(0) = 1

Understanding the NOR Gate

The NOR gate is a universal logic gate that produces an output of 1 (TRUE) only when both inputs are 0 (FALSE). It is the complement of the OR gate. The name NOR stands for "NOT OR" because the output is the negation of the OR operation. NOR gates are called "universal gates" because any other logic gate can be constructed using only NOR gates.

Logic Gate Comparison

NOR Gate

Output is 1 only when both inputs are 0.

NOR = NOT(A OR B)

OR Gate

Output is 1 when at least one input is 1.

OR = A OR B

NAND Gate

Output is 0 only when both inputs are 1.

NAND = NOT(A AND B)

NOR Truth Table

The NOR gate truth table for two inputs A and B:

  • A=0, B=0: NOR = 1 (both inputs are 0)
  • A=0, B=1: NOR = 0 (at least one input is 1)
  • A=1, B=0: NOR = 0 (at least one input is 1)
  • A=1, B=1: NOR = 0 (at least one input is 1)

NOR as a Universal Gate

Any Boolean function can be implemented using only NOR gates:

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

Applications

NOR gates are fundamental in digital electronics and computer architecture. They are used in memory circuits (SR latches), CPU design, programmable logic arrays, and various combinational and sequential circuits. The fact that NOR is a universal gate makes it particularly important in VLSI design and FPGA programming.