Binary Numbering System Examples

The binary numbering system, also known as base-2, represents numeric values using two symbols: 0 and 1. Each digit in a binary number is referred to as a bit. Binary numbers are the foundation of digital systems and computers, where binary logic is used to perform calculations and store data. Understanding binary is crucial for computer science and electronics. Below are examples demonstrating the binary system and conversion between binary and decimal systems.

Examples:

Binary to Decimal:

1. Binary: 1011

• Calculation: (1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0)
• Decimal: (8 + 0 + 2 + 1 = 11)

1. Binary: 1101

• Calculation: (1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0)
• Decimal: (8 + 4 + 0 + 1 = 13)

Decimal to Binary:

1. Decimal: 9

• Calculation: (9 \div 2 = 4 \text{ remainder } 1), (4 \div 2 = 2 \text{ remainder } 0), (2 \div 2 = 1 \text{ remainder } 0), (1 \div 2 = 0 \text{ remainder } 1)
• Binary: 1001

1. Decimal: 14

• Calculation: (14 \div 2 = 7 \text{ remainder } 0), (7 \div 2 = 3 \text{ remainder } 1), (3 \div 2 = 1 \text{ remainder } 1), (1 \div 2 = 0 \text{ remainder } 1)
• Binary: 1110