Binary to Decimal Converter

How to Convert Binary to Decimal?

To convert binary to decimal, multiply each binary digit by 2 raised to the power of its position (counting from right to left, starting at 0) and sum the results. For example: 1010₂ = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 8 + 0 + 2 + 0 = 10₁₀.

What is Binary?

Definition

Binary (base-2) is a numeral system that uses only two digits: 0 and 1. It is the fundamental language of computers and digital electronics.

Common Uses

• Computer data storage and processing
• Digital electronics and circuits
• Network communication protocols
• Machine code and assembly language
• Boolean logic and decision-making
• Error detection and correction codes

Structure

Each binary digit (bit) represents a power of 2. From right to left: 2⁰, 2¹, 2², 2³, etc. For example, 1010₂ = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10₁₀.

What is Decimal?

Definition

Decimal (base-10) is the standard numeral system used in everyday life. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Common Uses

• Everyday counting and arithmetic
• Financial calculations and currency
• Measuring quantities and dimensions
• Scientific calculations
• Data representation in most applications

History

The decimal system is believed to have originated from counting on fingers (humans typically have 10 fingers), making it the most intuitive and widely adopted numeral system.

Binary to Decimal Conversion Table

This table shows common binary to decimal conversions for quick reference.