Binary to Decimal Converter

Convert base-2 binary numbers to base-10 decimal numbers. Essential for computer science students, programmers, and digital electronics engineers.

Binary Number

Decimal Result

Step-by-Step Conversion

Understanding Binary to Decimal Conversion

Binary numbers use a base-2 system (digits 0 and 1), while decimal uses base-10 (digits 0-9). Each binary digit represents a power of 2, starting from the rightmost digit (2⁰).

Conversion Example: 1101

Write powers of 2 from right to left: 2³ 2² 2¹ 2⁰
Multiply each digit by its power: 1×8 + 1×4 + 0×2 + 1×1
Sum the results: 8 + 4 + 0 + 1 = 13

Binary Reference Table

Binary	Decimal	Binary	Decimal
0000	0	1000	8
0001	1	1001	9
0010	2	1010	10
0011	3	1011	11
0100	4	1100	12
0101	5	1101	13
0110	6	1110	14
0111	7	1111	15

Practice Converter

Enter a random binary number to practice:

Your conversion result:

Frequently Asked Questions

What is the maximum binary number this converter supports?

The converter handles up to 32-bit binary numbers (4,294,967,295 in decimal). For larger numbers, precision may be limited by JavaScript's number representation.

Can I convert fractional binary numbers?

This converter currently only supports integer conversions. Fractional binary numbers require handling negative powers of 2 after the binary point.

Why is binary important in computing?

Binary is fundamental because digital electronics use two voltage levels (high/low) that naturally correspond to 1 and 0. All computer data is ultimately represented in binary.

Note: This tool is for informational and educational purposes only. While we strive for accuracy, always verify critical conversions with professional tools.

References:

Binary number system fundamentals
Positional notation conversion methods
IEEE binary integer representation standards

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Binary to Decimal Converter - Base 2 to Base 10

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