Binary arithmetic is fundamental to the operation of digital systems, as all calculations in computers are performed using binary numbers (0s and 1s). Let's break down the main binary arithmetic operations: addition, subtraction, multiplication, and division.

1. Binary Addition

Binary addition works similarly to decimal addition, but it follows simpler rules due to the binary system having only two digits (0 and 1).
Rules for Binary Addition:



Example 1: Simple Binary Addition

Question:-  Add 1011 (11 in decimal) and 1101 (13 in decimal).

Step-by-step:

  • 1 + 1 = 10 (0 with carry 1)
  • 1 + 0 + carry 1 = 10 (0 with carry 1)
  • 0 + 1 + carry 1 = 10 (0 with carry 1)
  • 1 + 1 + carry 0 = 10 (0 with carry 1)

Result: 11000 (24 in decimal)


2. Binary Subtraction

Binary subtraction works similarly to decimal subtraction, but it requires borrowing from the next bit when needed. The key difference is that binary has only two digits, 0 and 1.

Rules for Binary Subtraction:


Example 1: Simple Binary Subtraction

Question:- Subtract 1010 (10 in decimal) from 1111 (15 in decimal).

Step-by-step:

  • 1 − 0 = 1
  • 1 − 1 = 0
  • 1 − 0 = 1
  • 1 − 1 = 0

Result: 0101 (5 in decimal)


3. Binary Multiplication

Binary multiplication is similar to decimal multiplication, but the process is simplified because you only multiply by 0 or 1.

Rules for Binary Multiplication:



Example 1: Simple Binary Multiplication

Multiply 1011 (11 in decimal) by 1101 (13 in decimal).

      1011
    × 1101
  ---------
      1011    (1011 × 1)
 +   0000     (1011 × 0, shift one place to the left)
 +  1011      (1011 × 1, shift two places to the left)
 + 1011       (1011 × 1, shift three places to the left)
  ---------
  10001111    (Result: 143 in decimal)