How to Convert Binary to Decimal Step by Step
Understand binary number systems and convert values to decimal using position-based multiplication—no shortcuts, just clarity.
Binary is a base-2 number system using only digits 0 and 1. Computers store all data in binary, but humans typically read decimal (base-10). Converting between them is a fundamental skill in programming and computer science.
Understanding Place Values
Each binary digit represents a power of 2, read from right to left: 20, 21, 22, 23, and so on. The decimal value is the sum of each bit multiplied by its place value.
Step-by-Step Example
Convert 1101 to decimal:
- 1 × 23 = 8
- 1 × 22 = 4
- 0 × 21 = 0
- 1 × 20 = 1
Sum: 8 + 4 + 0 + 1 = 13
Larger Numbers
For long binary strings, work systematically from right to left. Double-check each power of 2 - a common mistake is misaligning digit positions.
Related Developer Tools
For encoding data in web applications, explore our Base64 Encode and Base64 Decode tools.
Converting Decimal Back to Binary
The reverse process divides the decimal number by 2 repeatedly and reads remainders from bottom to top. For example, 13 divided by 2 gives remainders 1, 0, 1, 1 - reading upward produces 1101.
Where You Use This in Real Projects
Binary conversion appears in permission flags, color channel values, network subnet calculations, and low-level debugging. Understanding place values helps you read hex dumps and bitmask documentation even when you work in higher-level languages.
Key Takeaways
- Read binary digits right to left, multiplying by powers of 2
- Double-check alignment - one shifted digit changes the entire result
- Practice with short strings before tackling 16-bit or 32-bit values