How this calculation works
Each source digit contributes its value times a power of the source base. Repeated division by the destination base supplies output digits from right to left. Letters A through Z stand for digit values 10 through 35.
Value = Σ digit × base^position; rewrite that exact integer in the destination baseA worked example
FF in base 16 is 255 in base 10 and 11111111 in base 2. The sign, if present, is applied to the whole number.
Good to know
Whole numbers only, with at most 64 source digits. No fractional portion, bit width, two’s-complement interpretation or preservation of leading zeros. Invalid digits for the selected source base are rejected.
Reference: MIT OpenCourseWare: binary and hexadecimal representations (opens in a new tab) ↗
A numeral is a weighted list of digits
The chmod permission calculator interprets octal mode bits and a separate umask creation example. A numeric base conversion alone does not explain file access flags. Hexadecimal FF has two F digits, each worth 15. The right one contributes 15×16⁰ and the left one contributes 15×16¹, so the value is 255. In binary, the same whole number is 11111111. The quantity stays the same while its written representation changes.
The table shows input place values. For long inputs it displays only the rightmost twelve places to keep the page readable; the conversion still uses every entered digit.
The modular exponentiation calculator works with an integer value after its numeral base has been interpreted.
Choose the alphabet before interpreting letters
The source base controls which digits are legal. In base 12, B means eleven and C is invalid. In base 16, F means fifteen. The output uses uppercase A–Z for values ten through thirty-five.
A data size converter changes physical byte units such as MB and MiB. This page changes numeral notation only: base 2 is not a byte unit, and a hex value does not say how many bits or bytes a file occupies without an encoding.
Signed value is not a machine bit pattern
A leading minus sign describes a negative mathematical integer. It is not a two’s-complement encoding, a fixed-width register, or an interpretation of a signed byte. Leading zeros are not preserved because they do not change the integer.
The modular exponentiation calculator uses the integer value in a remainder calculation after you know what the numeral means. This converter itself performs no modular reduction.
A few questions, answered
Can I enter lowercase hexadecimal?
Yes. Letters are normalized to uppercase before digit validation.
What does base 36 add?
Digits 0–9 followed by letters A–Z, with Z worth 35.
Does this convert fractions?
No. Only whole-number numerals, with an optional minus sign, are supported.