Binary Subtraction Calculator
Subtract binary numbers using borrow or complement methods with step-by-step explanations
Binary Subtraction Calculator
Number of bits for result representation
Only 0s and 1s allowed
Only 0s and 1s allowed
Traditional borrowing method similar to decimal subtraction
Example Calculations
Borrow Method Example
Borrow when subtracting 1 from 0
Complement Method Example
Use two's complement and addition
Binary Subtraction Rules
Basic Rules
Borrowing
When subtracting 1 from 0, borrow 1 from the next left position. The borrowed 1 becomes 10 in binary (2 in decimal).
Method Comparison
Borrow Method
- • Similar to decimal subtraction
- • Intuitive and easy to understand
- • Direct borrowing process
Complement Method
- • Uses two's complement
- • Converts subtraction to addition
- • Common in computer systems
Binary Subtraction Tips
Align numbers by their rightmost digits
Remember: 0 - 1 requires borrowing
Two's complement method avoids borrowing
Negative results use two's complement
Understanding Binary Subtraction
Borrow Method
The borrow method is similar to decimal subtraction. When you need to subtract 1 from 0, you borrow 1 from the next position to the left, making it 10₂ (2₁₀) minus 1, which equals 1.
Steps:
- 1. Align the binary numbers
- 2. Start from the rightmost digit
- 3. If minuend digit ≥ subtrahend digit, subtract directly
- 4. If minuend digit < subtrahend digit, borrow from left
- 5. Continue until all digits are processed
Complement Method
The complement method converts subtraction into addition by using the two's complement of the subtrahend. This method is commonly used in computer systems.
Steps:
- 1. Align numbers to same bit width
- 2. Find one's complement (flip all bits)
- 3. Add 1 to get two's complement
- 4. Add minuend and two's complement
- 5. Remove overflow bit if present
Negative Results
When the subtrahend is larger than the minuend, the result is negative. In binary systems, negative numbers are typically represented using two's complement notation, where the most significant bit indicates the sign (1 for negative, 0 for positive).