# Binary Numbers.

## The Decimal Number System.

The Decimal numbering system is the one that is most familiar to us.
In the decimal system, a single digit is represented by one of ten possible symbols.
( 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9 ).

Quantities greater than nine are written using two or more digits. e.g.

- 12.
- 20.
- 230.

Each digit in the number carries a different “weighting”.

e.g. Consider the number 44. The left hand digit represents a larger quantity than the right hand digit, even though the symbols are the same.
(i.e. the left hand digit represents a quantity of forty, while the right hand digit represents a quantity of just four). One way of expressing this, is
to say that the left hand digit has a greater weighting than the right hand digit.

So the values of the digits in a number, depend both on the symbols used and their position in the number.

The symbol 2 in each of the above examples represents:

- Two in example i).
- Twenty in example ii).
- Two hundred in example iii).

The weightings of each position in a decimal number, increase by a factor of 10, as we move from right to left.
i.e. The right hand digit position has a weighting of 10^{0}, with the power increasing by one, for each position we move to the left.

e.g.

- in example i) the right hand digit value is, 2x 10
^{0} = 2 x 1 = 2.
- in example ii) the middle digit value is, 2x 10
^{1} = 2 x 10 = 20.
- in example iii) the left hand digit value is, 2x 10
^{2} = 2 x 100 = 200.

Because the right hand digit has the lowest weighting and the left hand digit has the greatest weighting, we say that the right hand digit, is the
least significant digit and the left hand digit, is the most significant digit.