Numbers are the foundation of bitcoin.  However, there are a few things you must get comfortable with before getting too involved in bitcoin.  If your aim is just to transact with bitcoins, then its not essential that you know this.  Just like driving a car, you might not need to know how an internal combustion engine works, but if you stall your car you have a better understanding why it stalled.

Bases or Radix

Bases or radixes in mathematical numeral systems is the number of unique digits including 0. In every day we use base 10.  Its a common theory that humans use base ten because of you have ten fingers, so I makes counting easy.  In computer science and bitcoin, we use a few different bases.

Base 16 or Hexadecimal or just “Hex” use the characters 0123456789ABCDEF to represent 0 to 15.

1 x 16^1 + 1 x 16^0

For 16, we add a 1 to the 16ths column and a zero to the ones column.  10.

Base 58 is only used in bitcoin as far as Im aware.  Characters that look similar omitted from the alphabet: 0 (zero), O (capital o), I (capital i) and l (lower case L).  As transactions are irreversible, it is extremely important you send bit coins to the correct address.  QR codes are often used to display bitcoin addresses, because they are easily machine readable.

The alphabet is 123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz  Note that the order is important.  Because both upper case and lower case characters have been used, the addresses are case sensitive.

Base 64 is used often in cryptography.

Modulus arithmetic or clock math