How to Add, Subtract, Multiply, and Divide Binary Numbers: Complete Tutorial

Introduction to Binary Arithmetic

Computers and digital microprocessors perform all fundamental logic and processing using the binary numbering system (Base-2), composed exclusively of two symbols: 0 and 1. Understanding how binary addition, subtraction, multiplication, and division work is essential for computer science students, software engineers, and electrical engineers.

You can perform operations and conversions across binary, decimal, octal, and hexadecimal using our free Binary Calculator.

Binary Addition Rules

Binary addition follows four simple rules:

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 0 (carry 1 to next column)
• 1 + 1 + 1 = 1 (carry 1 to next column)

Binary Addition Example: 1011 + 1101

    1 1 1   (carries)
    1 0 1 1  (decimal 11)
  + 1 1 0 1  (decimal 13)
  ----------
  1 1 0 0 0  (decimal 24)

Binary Subtraction Rules

Binary subtraction uses standard borrowing when subtracting 1 from 0:

• 0 - 0 = 0
• 1 - 0 = 1
• 1 - 1 = 0
• 0 - 1 = 1 (borrow 1 from the next higher bit)

Binary Multiplication

Binary multiplication is simpler than decimal multiplication because multiplying by 0 gives 0, and multiplying by 1 simply copies the number:

• 0 × 0 = 0
• 0 × 1 = 0
• 1 × 0 = 0
• 1 × 1 = 1

For complex binary calculations or verifying homework and digital circuit designs, use the Binary Calculator on UtiliVox.