➗ Binary Division Calculator
Divide two binary numbers with quotient and remainder
How to Use This Calculator
Enter Dividend and Divisor
Input the dividend (number to be divided) and divisor (number to divide by) in binary format. The calculator accepts only 0s and 1s. Examples: dividend = 1010, divisor = 10.
Click Calculate Division
Press the "Calculate Division" button to perform binary division. The calculator will compute the quotient and remainder, showing both binary and decimal results.
Review Results
The result shows the quotient and remainder in both binary and decimal formats. You'll also see a step-by-step breakdown of the division process.
Formula
Dividend ÷ Divisor = Quotient + (Remainder / Divisor)
Dividend = (Quotient × Divisor) + Remainder
How it works:
Binary division works similarly to decimal long division. The process involves repeatedly subtracting the divisor from portions of the dividend, determining how many times the divisor fits into each segment.
Binary Division Steps:
- Align the divisor with the leftmost bits of the dividend
- Compare: if divisor ≤ current portion, subtract and set quotient bit to 1
- If divisor > current portion, set quotient bit to 0
- Bring down the next bit and repeat
- Continue until all bits are processed
Example 1: 1010 ÷ 10 (10 ÷ 2 in decimal)
101 (quotient)
10) 1010
- 10
----
10
- 10
----
0 (remainder)
Result: Quotient = 101 (5), Remainder = 0
Example 2: 1101 ÷ 11 (13 ÷ 3 in decimal)
100 (quotient)
11) 1101
- 11
----
01
- 00
----
1 (remainder)
Result: Quotient = 100 (4), Remainder = 1
Frequently Asked Questions
How does binary division work?
Binary division uses the same long division algorithm as decimal division, but operates in base 2. You repeatedly compare the divisor with portions of the dividend, subtract when possible, and build the quotient bit by bit.
What happens when dividing by zero?
Division by zero is undefined and not allowed. The calculator will show an error message if you attempt to divide by zero (binary 0).
Can I divide binary numbers of different lengths?
Yes! The calculator handles binary numbers of any length. The division process works the same way regardless of length differences between dividend and divisor.
What is the relationship between quotient and remainder?
The relationship is: Dividend = (Quotient × Divisor) + Remainder. The remainder is always less than the divisor. This fundamental relationship holds true in both binary and decimal systems.
Why is binary division important in computer science?
Binary division is fundamental to computer arithmetic. Processors use division circuits to perform division operations. Understanding binary division helps in algorithm design, optimization, and understanding how computers perform mathematical operations.
How does binary division compare to decimal division?
The algorithm is identical, but binary division uses base 2 instead of base 10. This means you only work with 0s and 1s, making comparisons and subtractions simpler, but the fundamental process remains the same.