Binary to Decimal Converter

Binary numbers to Decimal conversion

Binary to Decimal Converter

How to Convert Binary Numbers to Decimal

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:

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

Example: Converting Number 1010

Binary number: 1010

1 × 2³ = 1 × 8 = 8
0 × 2² = 0 × 4 = 0
1 × 2¹ = 1 × 2 = 2
0 × 2⁰ = 0 × 1 = 0

Decimal number: 8 + 0 + 2 + 0 = 10

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.