# Bitwise NOR Calculator

URL: https://speedycalculator.com/calculators/math/bitwise-nor/
Last updated: 2026-10-30

> The bitwise NOR calculator applies NOR to two numbers bit by bit – entered in binary, octal or decimal – with a fixed bit width, and shows the result in binary, decimal (signed and unsigned), octal and hexadecimal. You can switch to the other bitwise operations too.

## Inputs

- Representation
- Number format
- Number 1
- Number 2
- Operation

## Results

- Result (binary)
- Result (decimal, unsigned)
- Result (decimal, signed two's complement)
- Result (octal)
- Result (hexadecimal)
- Bit by bit

## Formula

```
a NOR b is 1 only when both bits are 0 – the negation of OR; truth table: 0 0 → 1, 0 1 → 0, 1 0 → 0, 1 1 → 0
```

## Explanation

Bitwise operations work on each pair of bits independently. NOR is used for digital logic design: NOR is a universal gate from which every other gate (and the Apollo Guidance Computer) can be built. Programmers meet it in C, Java, Python and JavaScript as the ~(a | b) operator.

### How to use the Bitwise NOR Calculator

- **Representation**
- **Number format**
- **Number 1**
- **Number 2**
- **Operation**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Choose the bit width (representation) and the input format, then enter both numbers. They are padded to the chosen width, combined bit by bit and the result is shown in every common base. With a fixed width, the signed value uses two's complement.

## Worked example

Inputs — Representation: 8-bit; Number format: Binary; Number 1: 1011; Number 2: 0110; Operation: NOR.

Results — **Result (binary) = 1111 0000**; Result (decimal, unsigned) = 240; Result (decimal, signed two's complement) = -16; Result (octal) = 360; Result (hexadecimal) = F0; Bit by bit = 0000 1011
NOR 0000 0110
─────────
= 1111 0000.

## Key terms

- **Bit**: A binary digit, 0 or 1.
- **Bit mask**: A pattern of bits used to select or change other bits.

## FAQ

**What does bitwise NOR do?**
It compares two numbers bit by bit: a NOR b is 1 only when both bits are 0 – the negation of OR.

**Why choose a bit width?**
Operations like NOT, NOR and the signed value depend on how many bits the number has.

**Can I enter decimal numbers?**
Yes – choose Decimal as the number format.

**What is the difference between bitwise and logical NOR?**
Logical operators treat whole values as true/false; bitwise ones act on every bit separately.


## Sources

- [Wolfram MathWorld – Binary](https://mathworld.wolfram.com/Binary.html)
- [Harvard CS50 – Binary and bitwise operators](https://cs50.harvard.edu/x/)