Binary to Decimal Converter - Convert Binary to Decimal Online

Binary to Decimal Converter

The Binary to Decimal Converter instantly converts binary numbers (base-2) into their decimal (base-10) equivalents. This free online tool is ideal for students learning number systems, programmers working with low-level data, digital electronics engineers, and anyone who needs quick binary-to-decimal conversions.

Binary is the fundamental language of computers, using only two digits — 0 and 1. Every binary number corresponds to a unique decimal value, which is calculated by summing the place values of each bit position.

1101    → 13
1010    → 10
11111111 → 255
10000000 → 128

What is a Binary Number?

A binary number is a number expressed in the base-2 numeral system, which uses only two symbols: 0 and 1. Each digit in a binary number is called a bit. Binary numbers are the native language of computers, digital circuits, and microprocessors.

What is a Decimal Number?

A decimal number is a number expressed in the base-10 numeral system, which uses ten digits from 0 to 9. Decimal is the standard number system used in everyday mathematics, commerce, and most human communication.

How to Convert Binary to Decimal

1. Write down the binary number.
2. Identify the position of each bit from right to left (starting at position 0).
3. Multiply each bit by 2 raised to its position number.
4. Add all the resulting values together.

Binary to Decimal Formula

Decimal = Σ (bit × 2^position)

Position is counted from right to left, starting at 0.

Example

Binary = 1101

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

Decimal = 8 + 4 + 0 + 1 = 13

Binary to Decimal Conversion Table

Applications of Binary to Decimal Conversion

• Computer Programming
• Embedded Systems Development
• Digital Electronics
• Networking and IP Address Calculations
• Microcontroller and Microprocessor Design
• Data Encoding and Decoding
• Computer Science Education
• Low-level Debugging

Programming Examples

Python

int('1101', 2)

Output

13

JavaScript

parseInt('1101', 2)

Output

13

C / C++

strtol("1101", NULL, 2);

Frequently Asked Questions