Number Base Converter

Because they use ordinary JavaScript numbers, which are floating point and hold about 15 significant decimal digits. Parse 0xFFFFFFFFFFFFFFFF that way and you get 18446744073709552000, which is wrong in its last four digits and converts back to a different hex string entirely. Nothing is reported as an error; the answer is simply wrong. This one uses arbitrary precision, so a value of any length keeps every digit.

Because one hex digit is exactly four bits, so a byte is always two characters and never one and a bit. That makes a hex dump line up in columns and makes it trivial to read individual bits out of a value. Decimal has no such relationship with binary, which is why a memory address in decimal is unreadable and the same address in hex is not.

Mainly because Unix file permissions are three groups of three bits, and three bits is exactly one octal digit. That is the entire reason chmod 755 looks the way it does. Outside permissions and a few file formats it has largely been replaced by hexadecimal, which lines up with bytes rather than with three-bit groups.

How negative numbers are actually stored. Rather than reserving a sign bit and negating, the value is subtracted from two to the power of the width, so minus one in eight bits is 0xFF and in 32 bits is 0xFFFFFFFF. It has the useful property that addition and subtraction work identically on signed and unsigned values, which is why every current processor uses it. It is shown here for each common width when the value is negative.

Because digits run out. Ten numerals plus twenty-six letters is thirty-six symbols and there is nothing conventional left to borrow, so 36 is the highest base that can be written with one character per digit using the usual alphabet. Base 64 exists but needs a defined symbol set including punctuation, and encodes bytes rather than numbers.