Why these bases
Binary is what the machine uses. Hexadecimal is the readable form of it: one hex digit is exactly four bits, so a byte is always two characters and a colour or memory address stays legible. Octal maps to three bits and survives mainly in Unix file permissions.
Conversion between them is exact, because they are all powers of two. Decimal is the odd one out — which is why 0.1 has no exact binary representation and why floating-point arithmetic surprises people.
Negative numbers and width
A negative number in binary depends on how wide the register is: -1 is 11111111 in eight bits and thirty-two ones in a 32-bit integer. Without knowing the width, "the binary of -1" has no single answer, which is why two’s complement output always names its size.
Frequently asked questions
Why is hexadecimal used so much?
One hex digit is exactly four bits, so a byte is always two characters. It is binary that a human can read without counting.
What is the largest base supported?
Base 36 — the ten digits plus twenty-six letters. Beyond that there are no conventional symbols left.
How do I convert a negative number to binary?
You have to say how wide the register is. -1 is 11111111 in eight bits and thirty-two ones in a 32-bit integer.
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