Binary Converter
Convert binary, decimal, hex, and octal numbers with this free online base converter. Features instant bidirectional results with a visual comparison chart.
About This Calculator
The Binary Converter instantly translates numbers between binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8) number systems. Simply select your input base type, enter your number, and the converter displays the equivalent values across all four bases simultaneously in a clear comparison chart. This tool is designed for students learning computer science, programmers working with low-level systems, network engineers configuring IP addresses, and anyone who needs quick and accurate number base conversions.
Number base conversion works by interpreting the input numeral in its original base and then expressing that same quantity in the target base. For example, the binary number 1011 represents 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2&sup0; = 11 in decimal. Hexadecimal uses digits 0-9 and letters A-F, where A represents 10 and F represents 15. Octal uses digits 0-7. Understanding these systems is fundamental to digital electronics, memory addressing, color codes (hex), file permissions (octal), and data representation in computing.
Regional Notes
India (IN): Binary, decimal, hex, and octal conversions are used extensively in Indian computer science curricula (CBSE, ICSE, and university courses) and embedded systems industries. The decimal system is universally used for everyday arithmetic.
United States (US): Binary and hex conversions are core topics in US computer science programs (AP Computer Science, ACM curricula). Octal is less common but appears in Unix/Linux coursework and legacy system maintenance.
United Kingdom (UK): British computer science qualifications (GCSE, A-Level, degree programs) cover all four bases. Hex is widely used in web development for color codes (#FF5733) and memory addresses in debugging tools.
Frequently Asked Questions
How does the Binary Converter work?
Select the input number system (binary, decimal, hex, or octal), enter your number, and instantly see its equivalent in all other bases with a visual comparison chart.
What number systems are supported?
Binary (base 2), Decimal (base 10), Hexadecimal (base 16), and Octal (base 8) are all supported for bidirectional conversion.
How do I convert binary to decimal manually?
Multiply each binary digit (bit) by 2 raised to the power of its position from the right, starting at 0. For example, 1011 in binary = 1x8 + 0x4 + 1x2 + 1x1 = 11 in decimal.
What is FF in hexadecimal in decimal?
FF in hexadecimal equals 255 in decimal (15x16 + 15x1 = 240 + 15 = 255).
Is the binary converter free?
Yes, it is completely free to use with no registration or hidden charges.
How do I convert decimal to binary manually?
Divide the decimal number by 2 repeatedly and record the remainders in reverse order. For example, to convert 13 to binary: 13 divided by 2 = 6 remainder 1, 6 divided by 2 = 3 remainder 0, 3 divided by 2 = 1 remainder 1, 1 divided by 2 = 0 remainder 1, giving 1101.
Why is hexadecimal used in programming?
Hexadecimal (base 16) is used because it maps neatly to binary — each hex digit represents exactly four binary bits (a nibble). This makes hex much more readable than long binary strings. For instance, the binary 11111111 is FF in hex, and memory addresses like 0x7FFF is far easier to work with than its 15-bit binary equivalent.