A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. For example, base 10 (decimal) uses 10 digits (0-9), base 2 (binary) uses 2 digits (0-1), base 16 (hexadecimal) uses 16 symbols (0-9 and A-F). The value of each digit position is multiplied by the base raised to the power of its position index.

The general method is: Source Base → Decimal → Target Base. First, convert the number from its source base to decimal by multiplying each digit by the base raised to its positional power and summing the results. Then, convert the decimal value to the target base by repeatedly dividing by the target base and collecting remainders in reverse order. Our tool handles all of this instantly for bases 2 through 36.

For base N (where 2 ≤ N ≤ 36), valid digits are 0 through N-1. For bases greater than 10, letters A-Z represent values 10-35. For example, base 16 uses 0-9 and A-F (representing 10-15). Base 36 uses all digits 0-9 and all letters A-Z. Our converter automatically validates your input against the selected source base and alerts you if invalid characters are detected.

Binary (base 2) is the fundamental language of computers—all data is stored as bits (0s and 1s). Octal (base 8) was historically used in UNIX file permissions and is still found in some systems. Hexadecimal (base 16) is widely used to represent memory addresses, color codes (e.g., #FF5733), binary data in a more compact and human-readable form, and in programming/debugging. Each hex digit represents exactly 4 bits (a nibble), making conversion between hex and binary very straightforward.

Yes! Our converter uses BigInt arithmetic internally, which means it can accurately handle numbers far beyond JavaScript's standard Number limit (2⁵³ - 1). You can convert extremely long digit strings—such as a 50-digit hexadecimal value or a 100-bit binary number—with perfect precision. No rounding errors, no loss of accuracy.

The maximum base supported is 36. This is because we have exactly 10 digits (0-9) plus 26 letters (A-Z) in the English alphabet, giving us 36 unique symbols total—the maximum that can be represented with standard alphanumeric characters. Bases higher than 36 would require additional symbols beyond the standard 0-9, A-Z set. For most practical applications, bases 2, 8, 10, and 16 are the most commonly used.

In positional notation, each digit's contribution to the total value depends on its position. The rightmost digit is multiplied by base⁰ (which is 1), the next digit by base¹, then base², and so on. For example, the binary number 1101 = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13 in decimal. This principle applies identically to all bases.