Binary Division Calculator

Divide binary numbers, get quotient and remainder with step‑by‑step explanation. Ideal for computer architecture and digital logic students.

Binary Division Rules: Same as decimal long division, but with only digits 0 and 1. At each step, the divisor is either subtracted (if it “fits”) or not.

Number to be divided.
Number to divide by (must be > 0).
1101 ÷ 10 (13÷2)
1010 ÷ 11 (10÷3)
1111 ÷ 100 (15÷4)
1001 ÷ 11 (9÷3)
110 ÷ 10 (6÷2)
101101 ÷ 101 (45÷5)
Calculating...

Understanding Binary Division

Binary division follows the same “long division” algorithm we use in decimal, but with only two digits (0 and 1). It’s the basis for how CPUs perform division and is essential for understanding computer arithmetic.

? Manual Long Division (Decimal vs Binary)

Let’s divide 1101₂ (13) by 10₂ (2). The process: 

        ______
  10 | 1101     (1. divisor fits into first two bits? 10 ≤ 11 → yes)
        10       (subtract 10 from 11 → 1, bring down next 0)
        ---
          01     (10 does not fit into 1, write 0 in quotient)
           0      (bring down last 1)
           --  
           11     (10 fits into 11 → subtract 10 → 1, write 1 in quotient)
           10
           --
            1     (remainder)
  quotient = 110₂ (6), remainder = 1₂ (1)

⚙️ Algorithm Steps

  1. Take the first part of the dividend that is at least as large as the divisor.
  2. Write a 1 in the quotient (binary digit) and subtract the divisor from that part.
  3. Bring down the next bit from the dividend.
  4. Repeat: if the current remainder (after bringing down) is ≥ divisor, place a 1 and subtract; otherwise place a 0 and just bring down the next bit.
  5. Continue until all bits are processed. The final remainder is the remainder.

? Why it works

Because binary is a positional system, the same “trial subtraction” method works. At each step we are essentially checking if the divisor “fits” into the current partial remainder. This is exactly how hardware dividers (like in the ALU) operate, often using a shift‑subtract algorithm.

? Relationship with Decimal

You can always verify the result by converting to decimal:
dividend = quotient × divisor + remainder. Our calculator performs the division by converting to decimal (for speed and accuracy), but the binary result you see is exactly what you would obtain with long division.

Calculator notes:

  • ✅ Accepts binary strings of any length (up to 52 bits for exact decimal conversion).
  • ✅ Checks that divisor is not zero (division by zero is undefined).
  • ✅ Displays quotient, remainder, and decimal equivalents.
  • ✅ Example buttons let you quickly test typical cases.

❓ Frequently Asked Questions

Then the quotient is 0 and the remainder is the dividend itself. For example, 10₂ (2) ÷ 100₂ (4) gives quotient 0, remainder 10₂.

This calculator performs integer division (quotient and remainder). For fractional binary, you would need a separate fixed‑point division tool.

Most CPUs use a shift‑subtract algorithm (like the one shown above) in the arithmetic logic unit. Modern processors may use more efficient methods like SRT division.