Binary to Decimal Converter

Understanding Binary to Decimal Conversion

The binary number system (base-2) uses only two digits: 0 and 1. The decimal number system (base-10) uses ten digits: 0 through 9. Converting from binary to decimal involves understanding place values based on powers of 2. Each digit in a binary number represents a power of 2, starting from $2^0$ on the rightmost side.

How This Converter Works

This Binary to Decimal Converter takes your binary input and calculates its decimal equivalent. For example, the binary number $1101_2$ is converted as follows:

• $1 * 2^3 = 1 * 8 = 8$
• $1 * 2^2 = 1 * 4 = 4$
• $0 * 2^1 = 0 * 2 = 0$
• $1 * 2^0 = 1 * 1 = 1$
• Total: $8 + 4 + 0 + 1 = 13_{10}$

Our tool performs this calculation instantly when you enter a valid binary string (containing only 0s and 1s) and click "Convert".

Why Use This Tool?

• Accuracy: Avoid manual calculation errors.
• Speed: Get instant conversions for any binary number.
• Learning Aid: Helps understand the relationship between binary and decimal systems.
• Convenience: Easy-to-use online tool, no installation needed.
• Downloadable Results: Save your conversion for reference.

Use this free online Binary to Decimal Converter for quick and accurate conversions for programming, networking, or educational purposes.