Binary to Decimal Converter
Convert between binary and decimal numbers instantly. Also shows octal and hexadecimal values with step-by-step conversion explanations.
About Binary to Decimal Converter
This binary to decimal converter provides instant bidirectional conversion between binary (base-2) and decimal (base-10) numbers. It also displays the equivalent octal (base-8) and hexadecimal (base-16) representations, making it a complete number base conversion tool.
Real-Time Conversion
Enter a number in either the binary or decimal field and see all conversions update instantly as you type. The tool validates input in real time, ensuring binary input contains only 0s and 1s and decimal input contains only valid digits.
Step-by-Step Explanation
For each conversion, the tool displays a detailed step-by-step breakdown showing exactly how the math works. This makes it an excellent learning tool for students studying number systems, computer science, or digital electronics.
Bit Visualization
A visual display shows individual bits with their positional values (powers of 2), making it easy to see how each bit contributes to the final decimal value. Active bits are highlighted so you can quickly identify which powers of 2 are present in any number.
Common Use Cases
- Learning binary number systems for computer science courses
- Debugging bitwise operations in programming
- Converting between bases for networking and IP address calculations
- Understanding how computers store and represent numbers
All calculations run entirely in your browser with no data transmitted to any server.
Frequently Asked Questions
How do you convert binary to decimal?
Each binary digit represents a power of 2 based on its position from right to left, starting at 2^0. Multiply each digit by its corresponding power of 2, then add all the results. For example, binary 1011 equals (1x8) + (0x4) + (1x2) + (1x1) = 11 in decimal.
How do you convert decimal to binary?
Repeatedly divide the decimal number by 2 and record the remainder at each step. Read the remainders from bottom to top to get the binary representation. For example, 13 divided by 2 gives remainders 1, 0, 1, 1 (reading bottom to top), so 13 in binary is 1101.
What is the relationship between binary, octal, and hexadecimal?
All are positional number systems with different bases. Binary is base-2 (digits 0-1), octal is base-8 (digits 0-7), and hexadecimal is base-16 (digits 0-9, A-F). Octal groups binary digits in sets of 3, while hexadecimal groups them in sets of 4, making conversions between these bases straightforward.
What is the largest binary number this tool can handle?
The tool supports numbers up to what JavaScript can represent safely. For integers, this means up to 2^53 - 1 (9,007,199,254,740,991 in decimal, or 53 binary digits). For most practical purposes including programming and networking, this range is more than sufficient.