NUM­BER KNOW HOW

Stanthorpe Border Post - - LIFE -

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) =

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