Binary to Decimal Converter

Convert binary numbers into their equivalent decimal values with the Binary to Decimal Converter. Find the accurate decimal number instantly!

Binary to Decimal Conversion Tool

Binary Number:

Enter binary digits (0-1) with optional decimal point

Decimal Result:

Character count: 0

How To Convert Binary To Decimal Online

The interface of the binary to decimal conversion tool is easy to navigate for all users. It is designed to provide the following functions:

Step-by-Step Process:

Enter Binary Number: Type or paste your binary number in the input field
Click Convert: Press the "Convert to Decimal" button
Get Result: Your decimal equivalent appears instantly
Copy/Download: Save your result using copy or download features

Key Features:

Instant conversion with real-time results
Supports both whole and fractional binary numbers
Character count tracking
Copy to clipboard functionality
Download results as text file
Mobile responsive design

How to Convert Binary to Decimal Manually with Examples

To convert binary to decimal, each digit in the binary number is multiplied by 2 raised to the power of its position (from right to left, starting at 0). And then all the results are added together. This method allows you to accurately turn any binary value into a readable decimal format.

Binary to Decimal Conversion Formula:

Decimal = Σ(i=0 to n-1) bi × 2ⁱ

Explanation:

b_i = the binary digit (0 or 1) at position i, starting from the right (least significant bit)
2ⁱ = 2 raised to the power of the position index i
n = total number of binary digits

Example 1: Whole Number

Binary Number: 110010111

= (1 × 2⁸) + (1 × 2⁷) + (0 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰)
= 256 + 128 + 0 + 0 + 16 + 0 + 4 + 2 + 1
= 407 Decimal

Example 2: Fractional Number

Binary Number: 1000110.11

Whole part (1000110):
= (1 × 2⁶) + (0 × 2⁵) + (0 × 2⁴) + (0 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰)
= 64 + 0 + 0 + 0 + 4 + 2 + 0 = 70

Fractional part (.11):
= (1 × 2⁻¹) + (1 × 2⁻²) = 0.5 + 0.25 = 0.75

Final Result: 70.75 Decimal

Binary to Decimal Conversion Table

4-bit Binary to Decimal

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

8-bit Binary to Decimal

Binary	Decimal
00000000	0
00000001	1
00000010	2
00000100	4
00001000	8
00010000	16
00100000	32
01000000	64
10000000	128
11111111	255

Frequently Asked Questions

Binary to decimal conversion is the process of translating binary numbers (sequences of 0s and 1s) into their equivalent decimal (base-10) representation. Each binary digit represents a power of 2, and the conversion involves summing these values to get the final decimal result.

Our binary to decimal converter is 100% accurate. It uses precise mathematical algorithms to convert each binary digit to its corresponding decimal value, ensuring perfect conversion every time. The tool supports both whole numbers and fractional binary numbers with decimal points.

Yes! Our converter supports fractional binary numbers with decimal points. For example, you can convert binary numbers like "1000110.11" which would result in "70.75" decimal. The tool handles both the whole part and fractional part separately and combines them for the final result.

The converter supports binary inputs up to 1000 characters in length. This allows you to convert very large binary numbers while maintaining accuracy. For extremely large numbers, we recommend breaking them into smaller chunks.

Yes, our binary to decimal converter is completely free to use with no limitations. You can convert as many binary numbers as you need, as often as you need, without any registration or payment required. We believe in providing free, accessible tools for everyone.

Yes! We also offer a decimal to binary converter tool that allows you to convert decimal numbers back to binary format. You can find it in our tools section along with other binary conversion utilities like binary to ASCII and binary to hex converters.

About Binary to Decimal Conversion

Understanding Binary Numbers

Binary numbers are the fundamental language of computers, consisting of sequences of 0s and 1s. Each binary digit represents a power of 2, making it a base-2 number system. Understanding binary to decimal conversion is essential for computer programming, digital electronics, and data analysis.

Practical Applications

Binary to decimal conversion has numerous practical applications in computer programming, digital electronics, networking, and data analysis. Programmers often need to convert binary data to decimal for debugging, while network engineers use it for IP address calculations and subnetting.

Learning Benefits

Learning binary to decimal conversion helps students and professionals understand how computers process and store numerical data. It's a fundamental concept in computer science education and essential knowledge for anyone working with digital systems, programming languages, or computer architecture.

Professional Use

Professionals in fields like software development, cybersecurity, and digital systems regularly work with binary data. Our converter provides a quick and accurate way to translate binary representations into human-readable decimal numbers, making it an invaluable tool for technical work and problem-solving.