Michael Maardt: PC since 1984 • on the net since 1990.

16-number system

(A) Number values can also be represented by other number systems. In the computer world, numbers to base 16 are used a lot. The system many of us had banged our heads into at school is the normal decimal system to base 10.

0123456789 and then (because we haven?t any more symbols [fingers or toes]) we set 0 in the first place, to the right, and put a 1 in the second place, to the left, and we have 10.

Hexadecimal, the base 16 system, looks like this: 0123456789ABCDEF and only then ? with the value we write as 16 ? do we come to 10.

In the base 10 system, we say: the last cipher is the 1s, the next is the 10s, the next is the 100s and so on. In base 16 (because we are still thinking in terms of base 10), we say the units go as high as F (=15), the "10s" are the 16s, the "100s" are the 256s and so on. Now that's not so difficult, is it?

The decimal system is inappropriate for computer operations. It is a relic from man?s early days, when we thought using 10 fingers.

binary

10

16

00010000

16

10

00100010

34

22

11111111

255

FF

 

256

100

 

65536

10000

 

1048576

100000

The computing world handles large values and the hexadecimal system has proved its worth. Numbers are shown with a final "h," e.g. A0000h. The last zero is often dropped, so the above becomes A000h, which in the decimal system is the familiar 640 KB = 640 x 1024 bytes = 655360 bytes.

With the Windows calculator (choose View, Scientific) you can amuse yourself with these numbers and convert them easily.

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You are on michaelmaardt.com • © Michael Maardt 21. Jul. 2018