# Binary Division Calculator

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

> The binary division calculator divides one binary number by another and gives the quotient and remainder in binary and decimal.

## Inputs

- Dividend (binary)
- Divisor (binary)
- Representation

## Results

- Quotient (binary)
- Remainder
- Quotient (decimal)
- Dividend in decimal
- Divisor in decimal
- Method

## Formula

```
Dividend = divisor × quotient + remainder,  0 ≤ remainder < divisor
```

## Explanation

Binary long division follows the same steps as decimal long division, but each quotient digit is simply 0 or 1: the divisor either fits or it doesn't. Division by powers of two is just a right shift.

### How to use the Binary Division Calculator

- **Dividend (binary)**
- **Divisor (binary)**
- **Representation**

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

### How it works

Enter the dividend and divisor in binary. The quotient is the whole-number part and the remainder is what is left over.

### Tips

- Choose a bit width (8, 16, 32 …) so negative numbers and overflow are shown correctly.
- Group binary digits in fours – each group is one hexadecimal digit.
- The leftmost bit is the sign bit in two's complement.
- Everything is calculated exactly with whole-number arithmetic in your browser.

### Common mistakes to avoid

- Reading a signed number as unsigned (or the reverse).
- Forgetting to add 1 when forming a two's complement.
- Dropping leading zeros that matter for a fixed bit width.

## Worked example

Inputs — Dividend (binary): 101101; Divisor (binary): 101; Representation: Automatic (fit the numbers).

Results — **Quotient (binary) = 1001**; Remainder = 0 (0); Quotient (decimal) = 9; Dividend in decimal = 45; Divisor in decimal = 5; Method = Long division in base 2: bring down one bit at a time; the quotient bit is 1 whenever the divisor fits..

## Key terms

- **Remainder**: What is left after whole-number division.

## FAQ

**What is 101101 ÷ 101?**
1001 (45 ÷ 5 = 9), remainder 0.

**How do I divide by 2 in binary?**
Shift right by one place; the dropped bit is the remainder.

**Can the result have a fractional part?**
Yes, as a binary fraction; this calculator gives quotient and remainder.

**What happens when dividing by zero?**
It is undefined.

**What formula does the Binary Division Calculator use?**
Dividend = divisor × quotient + remainder,  0 ≤ remainder < divisor.


## Sources

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