Free NOR Calculator

Bitwise NOR Calculator: A Digital Logic Tool

A binary NOR calculator (sometimes called a NOR logic converter) is a free online logic gate calculator that determines the bitwise NOR output for a pair of numbers. NOR gates are essential building blocks in digital electronics, and this tool lets you quickly apply the NOR operation to integers in binary, octal, or decimal form. Like other bitwise calculators (NAND, XOR, XNOR), it processes numbers on a bit‑by‑bit basis, but follows the specific rules of the NOR gate.

How the NOR Gate Works

When you enter two numbers, the calculator first converts them to binary if they are not already in that format. It then compares each corresponding bit position, from the most significant to the least significant, applying the NOR rule:

• If both bits are 0, the output bit becomes 1.
• If at least one bit is 1, the output bit becomes 0.

The resulting binary sequence has the same number of bits as the inputs. For example, two 5‑bit numbers will yield a 5‑bit result. The tool handles multiple input formats—binary, octal, and decimal—so you can work in whatever system is most convenient.

NOR Gate Truth Table

The two‑input NOR gate behavior is captured in the truth table below:

A	B	NOR Output
0	0	1
0	1	0
1	0	0
1	1	0

The NOR gate is essentially the inverse of the OR gate: it produces a 1 only when both inputs are 0; for all other combinations the output is 0.

Worked Example

Suppose we have two 4‑bit binary numbers:

$$A = 1001_2,\quad B = 0101_2$$

Applying the NOR operation from left to right:

1. Bits (1, 0) → at least one 1 → output 0
2. Bits (0, 1) → at least one 1 → output 0
3. Bits (0, 0) → both 0 → output 1
4. Bits (1, 1) → at least one 1 → output 0

Thus the final NOR output is 0010 (binary). The calculator presents the result in binary alongside its decimal and octal equivalents, making it easy to interpret.

Using the NOR Logic Calculator

To obtain the NOR output for two numbers, follow these steps:

1. Select the bit width (e.g., 8 bits covers decimal values from –128 to 127 for signed numbers).
2. Choose the input format – binary, octal, or decimal.
3. Enter the two numbers you wish to compare.
4. The tool displays the NOR result immediately in binary, decimal, and octal formats.

Comparison with Other Bitwise Operators

NOR is one of several fundamental logic gates. Understanding how it differs from other gates is key to digital design:

• AND – outputs 1 only when both inputs are 1.
• OR – outputs 1 when at least one input is 1.
• NOT – inverts a single input.
• NAND – outputs 0 only when both inputs are 1; otherwise 1.
• XOR – outputs 1 when the inputs differ.
• XNOR – outputs 1 when the inputs are the same.

NOR is functionally complete (a universal gate), meaning any Boolean function can be implemented using only NOR gates. This property, shared with NAND, makes NOR a cornerstone of digital circuit synthesis.

Whether you are learning logic gates, verifying a design, or just need a quick bitwise NOR result, this bitwise NOR calculator provides an accurate and easy‑to‑use solution.