The Decimal System is a positional numbering system that represents the numbers in base 10, thus using ten different symbols. The decimal word originates in Latin, decem which means precisely ten. The specialists and historians are unanimous in considering that this way of counting in base 10, is due to the ten fingers that we have in the hands. This system uses the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These figures are called Indo-Arabic because they originated in the works initiated by Hindus and Arabs. In the decimal system, each set of ten units forms a new order. For example, ten tens are equivalent to a hundred; ten hundreds equals a thousand, and so on.
The Hexadecimal System is a positional numbering system that represents the numbers in base 16, thus using sixteen different symbols. This system uses the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 of the decimal system in addition to the letters A, B, C, D, E and F. The Hexadecimal System was created with purpose of minimizing the representation of a binary number. For example, the decimal number 2500 requires twelve digits to be represented in the binary system. But if the hexadecimal system is used, the same number only needs three digits, since 2500 equals 9C4. This represents a quarter of the digits used by the binary system. Normally, to distinguish a number in decimal number from a number in hexadecimal numbering, the latter uses the cardinal symbol to precede the number. Therefore, we consider that 45 is in decimal numbering, while #45 is in hexadecimal numbering.