Binary to Decimal Converter – Instant Base-2 to Base-10 Conversion
The Binary to Decimal Converter instantly transforms any binary (base-2) number into its decimal (base-10) equivalent. Whether you're a student learning number systems or a developer working with low-level data, this tool gives you fast and accurate results. Simply enter your binary string and the decimal value appears in real time.
Enter a binary number using only 0s and 1s.
Display the positional breakdown of each bit.
Your results will appear here
How to Use This Calculator
1. Type or paste your binary number into the 'Binary Number' field — use only the digits 0 and 1. 2. Choose whether you want to see the positional breakdown by selecting Yes or No under 'Show Breakdown'. 3. The Decimal Value, Hexadecimal, Octal equivalents, and the bit-by-bit breakdown are all displayed instantly below. 4. If you enter any invalid character, the Status field will alert you so you can correct the input.
How Binary to Decimal Conversion Works
Binary is a base-2 number system that uses only two digits — 0 and 1. Each digit (called a bit) represents a power of 2, starting from 20 on the right and increasing as you move left.
The Positional Value Method
To convert a binary number to decimal, multiply each bit by its corresponding power of 2 and sum the results. For example:
- 1010 = 1×23 + 0×22 + 1×21 + 0×20
- = 8 + 0 + 2 + 0 = 10
General Formula
For a binary number with digits bnbn-1...b1b0:
Decimal = Σ (bi × 2i) for i from 0 to n.
Additional Conversions Provided
This tool also shows the hexadecimal (base-16) and octal (base-8) equivalents. Hexadecimal groups bits by 4 and octal groups bits by 3, making them compact shorthand for binary.
- Binary 1111 → Decimal 15 → Hex F → Octal 17
- Binary 11111111 → Decimal 255 → Hex FF → Octal 377
Why Binary Matters
Every computer ultimately stores and processes data in binary. Understanding binary-to-decimal conversion is foundational for programming, computer architecture, networking (IP addresses, subnet masks), and digital electronics.