Base Converter
Convert between binary, decimal, hexadecimal, and octal number systems.
Utility
Base Converter
Generated on April 24, 2026
?What is the Base Converter?
A base converter translates integer numbers between positional numeral systems — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Each system expresses the same underlying value using different digits and place values. This tool is essential for programmers working with memory addresses and bitmasks, electronics engineers reading logic levels, computer-science students learning number theory, and web designers decoding hex colors. It handles any value between the supported bases and lets you see all four representations at once.
The Formula
In any positional system, each digit is multiplied by its base raised to the power of its position, and the products are summed. The rightmost digit is position 0, the next is position 1, and so on. To move between bases, the calculator parses the input into a single decimal value, then repeatedly divides by the target base — the remainders at each step become the target-base digits, read from bottom to top.
Practical Examples
255 in decimal equals FF in hex, 11111111 in binary, and 377 in octal — the maximum value of a single byte.
1024 in decimal equals 400 in hex and 10000000000 in binary — 2^10, the classic computing boundary.
Hex color #FF0000 equals RGB (255, 0, 0), which is pure red — each hex pair represents one 0-255 color channel.
Binary 1010 equals decimal 10 — a small illustrative example useful for teaching.
Memory address 0x7FFFFF in hex equals 8,388,607 in decimal — useful when debugging low-level code or embedded systems.
Unicode code point U+1F600 (the grinning face emoji) is hex 1F600 = decimal 128,512 — used when working with character encoding.