How positional bases work
In base 10 each place is worth ten times the one to its right: 255 = 2 × 100 + 5 × 10 + 5 × 1. In base 2 each place is worth twice the last, so 11111111 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. Bases above 10 need extra digits: hexadecimal uses A to F for 10 to 15, and base 36 uses all ten digits and 26 letters.
Converting by hand
To convert from decimal, divide repeatedly by the target base and read the remainders from the last to the first. 255 ÷ 16 = 15 remainder 15, and 15 ÷ 16 = 0 remainder 15, so 255 is FF in hex. To convert to decimal, multiply each digit by its place value and add.
Binary and hex convert directly in groups: each hex digit is exactly four binary digits (F = 1111, A = 1010), and each octal digit three. That is why programmers write bytes as two hex digits.
Where you see them
Hexadecimal appears in web colors (#FF8800), MAC addresses, memory addresses and Unicode code points. Octal survives in Unix file permissions (chmod 755). Binary underlies all digital data; a byte is eight bits, 0 to 255. Base 36 is used for compact IDs such as short links.