2.05 Number Systems (First of Four Parts: Decimal)

Representation of a quantity

Decimal: system based on 10

10 symbols: 0,1,2,3,4,5,6,7,8,9

Powers of 10

To explain binary and hexadecimal, we begin with decimal. All of these are number systems, which are the coding step to represent quantities. There are many ways of representing a quantity. Humans use the decimal number system; computers and data communication systems use the binary number system.

Decimal is a number system based on tens. There are ten symbols in the decimal number system: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Quantities are represented as powers of ten.

When expressing quantities in the decimal number system, we use a shorthand notation to indicate how many of which powers of ten are needed to make up the quantity.

For example, when we write the number “1967”, what we mean is
1 x 10^{3} + 9 x 10^{2} + 6 x 10^{1 } + 7 x 10^{0 } .

This could also be written as
(1 x 1000) + (9 x 100) + (6 x 10) + (7 x 1) .

The digits 1, 9, 6, and 7 indicate, for the appropriate power of 10, how many of that power of ten go in to making up the quantity.

In other words, the numbers 1, 9, 6 and 7 are placeholders in our shorthand notation, indicating how many of the powers of ten in that place go in to making up the quantity.