Binary Arithmetic

Overview

Binary arithmetic forms the foundation of all digital computer operations. Understanding how to perform basic mathematical operations in binary is crucial for digital design and computer architecture. The simplicity of binary arithmetic (using only 0s and 1s) makes it ideal for electronic implementation, though it requires more digits than decimal representation.

Detailed Explanation

Addition Rules

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 (carry 1)

Example:
  1101 (13)
+ 0111 (7)
-------
 10100 (20)

Subtraction Rules

0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 (borrow 1)

Example:
  1101 (13)
- 0111 (7)
-------
  0110 (6)

Multiplication

Rules same as decimal:
- Multiply by 0 → 0
- Multiply by 1 → same number

Example:
    1101 (13)
  × 0011 (3)
  -------
    1101
   1101
  -------
   100111 (39)

Division

Example: 1100 ÷ 11
   100
11)1100
   11
   --
    00
    00
    --
     00

Practice Problems

1. Perform binary addition:
   • 1010 + 1011
   • 1111 + 0001
   • 1100 + 1100

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