# Binary Addition Calculator

URL: https://speedycalculator.com/calculators/math/binary-addition/
Last updated: 2026-10-30

> The binary addition calculator adds two binary numbers, shows the long addition with carries, and gives the sum in binary and decimal – with an optional fixed bit width to see overflow.

## Inputs

- Binary number 1
- Binary number 2
- Representation

## Results

- Sum (binary)
- Sum (decimal)
- Number 1 in decimal
- Number 2 in decimal
- In the chosen bit width
- Long addition

## Formula

```
0 + 0 = 0,  0 + 1 = 1,  1 + 1 = 10 (write 0, carry 1),  1 + 1 + 1 = 11
```

## Explanation

Binary addition works like decimal addition but carries at 2 instead of 10. It is what the adder circuits inside every CPU do billions of times a second.

### How to use the Binary Addition Calculator

- **Binary number 1**
- **Binary number 2**
- **Representation**

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

### How it works

Enter two binary numbers. The calculator writes the column addition with the carry row. Choose a bit width to see how the result looks in a fixed-size register and whether it overflows.

## Worked example

Inputs — Binary number 1: 1011; Binary number 2: 111; Representation: Automatic (fit the numbers).

Results — **Sum (binary) = 1 0010**; Sum (decimal) = 18; Number 1 in decimal = 11; Number 2 in decimal = 7; Long addition = carry 111
01011
+ 00111
─────
10010.

## Key terms

- **Carry**: A 1 passed to the next column when a column sum is 2 or 3.

## FAQ

**What is 1 + 1 in binary?**
10.

**What is 1011 + 111?**
10010 (11 + 7 = 18).

**What is overflow?**
When the sum needs more bits than the register has.

**How do I check a binary sum?**
Convert both numbers and the result to decimal.


## Sources

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