Number Base Converter
A number base converter translates values between different numeral systems such as binary, octal, decimal, and hexadecimal. These conversions are fundamental in computer science, digital electronics, and programming, where data is stored and processed in binary but often displayed in more human-readable formats.
Understanding number bases helps developers debug low-level code, work with memory addresses, define colors in web design, and interpret network protocols. While decimal (base 10) is the system we use daily, computers operate in binary (base 2), and hexadecimal (base 16) provides a compact representation of binary data.
How it works
To convert from any base to decimal: multiply each digit by its base raised to its positional power and sum the results. For example, binary 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 11 in decimal. To convert from decimal to another base, repeatedly divide by the target base and collect remainders.
Use cases
- Converting between binary, hex, and decimal for programming tasks
- Working with hexadecimal color codes in web design and CSS
- Debugging memory addresses and bitwise operations in low-level code
- Understanding and interpreting network packet data and IP addresses
Frequently asked questions
How do I convert a binary number to decimal?
Multiply each binary digit by 2 raised to its position, counting from 0 on the right, and add the results. For example, 1011 equals 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11. This converter applies the same positional method for any base you choose.
How do I convert decimal to hexadecimal by hand?
Divide the decimal number by 16 repeatedly and record each remainder, using letters A–F for remainders 10–15. Reading the remainders from last to first gives the hex value. For example, 255 ÷ 16 = 15 remainder 15, and 15 ÷ 16 = 0 remainder 15, so 255 in decimal is FF in hexadecimal.
Why do programmers use hexadecimal instead of binary?
Hexadecimal is a compact shorthand for binary: each hex digit represents exactly four binary bits, so a 32-bit value shrinks from 32 characters to just 8. That makes memory addresses, color codes, and byte values far easier to read, compare, and type without losing the direct mapping to the underlying bits.
What do the prefixes 0x, 0b, and 0o mean in programming?
They mark the base of a literal number in most programming languages: 0x precedes hexadecimal (0xFF is 255), 0b precedes binary (0b1011 is 11), and 0o precedes octal (0o17 is 15). The prefixes exist so the compiler and human readers know 10 in the source code means ten, not binary two or octal eight.
What is octal used for today?
Octal (base 8) is less common than hex, but it survives in Unix and Linux file permissions, where a mode like 755 encodes read, write, and execute bits for owner, group, and others. Each octal digit maps to exactly three binary bits, which fits the three-bit permission groups perfectly.