How do you convert binary to decimal?

To convert binary to decimal, multiply each binary digit by its corresponding power of 2 (starting from 2^0 on the right) and sum the results. For example, binary 1011 = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 in decimal.

Can I convert negative binary numbers?

Yes, but you need to know the representation format. Common formats include sign-magnitude, one's complement, and two's complement. Our converter handles unsigned binary numbers by default. For signed numbers, you may need to specify the bit width and representation format.

Why is binary to decimal conversion important?

Binary to decimal conversion is essential because computers store and process data in binary format, but humans typically work with decimal numbers. Understanding this conversion helps bridge the gap between human-readable numbers and machine representation.

What is the difference between binary and decimal number systems?

Binary uses base 2 (only digits 0 and 1), while decimal uses base 10 (digits 0-9). Binary is fundamental to digital electronics because electronic circuits can easily represent two states (on/off, high/low voltage). Decimal is more intuitive for humans as it matches our counting system.

How accurate is this binary to decimal converter?

Our converter provides 100% accurate results for valid binary inputs. It handles binary numbers of any length and correctly converts them to their decimal equivalents. For very large numbers, JavaScript's number precision limits may apply, but for practical purposes, the conversions are accurate.

🔢 Binary to Decimal Converter

Convert binary numbers to decimal instantly. Free online binary to decimal converter with detailed steps for quick and accurate conversions.

Binary Input

Conversion: Binary → Decimal

Binary to decimal conversion is a fundamental operation in computer science and digital electronics. Binary numbers use only two digits (0 and 1), while decimal numbers use ten digits (0-9). This converter helps you quickly transform binary representations into their decimal equivalents, which is essential for understanding how computers process and store data.