# NUMBER KNOW HOW

Base numbers

OUR everyday number system is a Base-10 system because it uses 10 as its base number. It is also known as the decimal system – deci means 10.

The symbols 0,1, 2, 3,4, 5,6, 7, 8, and 9, are used to create numbers in the base 10 decimal number system, using place value and a decimal point to separate whole numbers from fractions.

A base number is the basis of a place value number system. In the Base-10 system each place is 10 times larger than the place to its right.

But you don’t have to use 10 as a Base. You could use 2 (Binary) or even 16 (Hexadecimal).

Try this

USING hexadecimal as a base means every number place is 16 times bigger.

Hexadecimal numbers look the same as the decimal numbers up to 9, but then there are the letters A,B,C,D,E,F in place of the decimal numbers 10 to 15. Hexadecimal: 0 1 2 3 4 5 6789ABCDEF Decimal: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Example:

4B5

■ The 4 is in the 16×16 position, so that means 4 ×16×16

■ The B (11) is in the 16 position, so that means 11 ×16

■ The 5 is in the 1 position so that means 5.

Answer: 4B5 = 4×16×16 + 11×16 + 5 =1205 Decimal

Your turn

Work out the decimal values of these hexadecimal numbers. 23 = (2x16 +3) =

1CE= (1 x16x16 + 12x16 + 14) =

A59C = (10x16x16x16 + 5x16x16 + 9x16 + 12) =