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.
Formula
Dividend = divisor × quotient + remainder, 0 ≤ remainder < divisorWorked 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.
Frequently asked questions
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.