• While people generally represent numbers in a decimal system (i.e. based on the number ten), computers generally perform computations in base 2 (the binary system).

• For "ease of representation" some computers display their binary number representations in base 8 (octal) or base 16 (hexadecimal).

• Carefully distinguish between a numeric value and a number representation.
  • A value is a measure of an attribute of collection of objects - it is an adjective!
  • A representation is the means by which we display a value and use in the manipulation of values.
  • Computers can only contain representations of numbers.

• To understand how a computer does arithmetic and to understand some of the limitations of computers,
  WE NEED TO UNDERSTAND BINARY REPRESENTATION SYSTEMS AND BINARY ARITHMETIC.
  But as Computer Scientists we are mostly interested in the ALGORITHMS of representation and usage.

See:

• Numeral systems
• Arabic numerals
• Roman numerals
• The Roman Art of Counting
• What is a "radix"?