Binary Number Converter

What is Binary Number System?

Binary number system is a positional numeral system with base 2, using only two digits: 0 and 1. All computers and digital devices operate with binary numbers, making understanding binary to decimal conversion critically important.

Algorithm for Converting Binary to Decimal

To convert a binary number to decimal, use the positional value formula:

1. Each position has a power of 2 value (right to left: 2⁰, 2¹, 2², 2³...)
2. Multiply each digit by the corresponding power of two
3. Add all the resulting products

Example: Converting Number 1010

Applications of Binary Code

• Programming — bitwise operations and masks
• Computer Architecture — processors and memory
• Network Technologies — IP addressing and protocols
• Digital Signal Processing — data encoding
• Embedded Systems — microcontrollers and IoT

Popular Binary Numbers

Some binary numbers are especially common:

• 11111111 = 255 (maximum value for 8 bits)
• 10000000 = 128 (most significant bit for 8-bit number)
• 1111 = 15 (maximum value for 4 bits)
• 1100 = 12 (commonly used in networking)

Quick Conversion with Calculator

Our online converter instantly translates any binary number to decimal. Simply enter the binary number and get the result with detailed explanation of each calculation step.