Java Reference
In-Depth Information
Computer Arithmetic
In the chapters of this topic, we have deliberately kept discussion of arithmetic to a minimum. However,
it is important overall and fundamental to understanding how some operators work, so I have included
a summary of the subject in this appendix. If you feel confident about your math knowledge, this will all
be old hat to you and you need read no further. If you find the math parts tough, then this section
should show you how easy it really is.
Binary Numbers
First let's consider what we mean when we write a common everyday number such as 321 or 747. Put
more precisely we mean:
321 is:
3 x 10 x 10 + 2 x 10 + 1
and 747 is:
7 x 10 x 10 + 4 x 10 + 7
Because it is built around powers of ten, we call this the decimal system (derived from the Latin
decimalis
meaning
of tithes
, which was a tax of 10% - ah, those were the days...).
Representing numbers in this way is very handy for people with ten fingers and ten toes, or creatures
with ten of any kind of appendage for that matter. However, your PC is quite unhandy in this context,
being built mainly of switches that are either on or off. This is OK for counting up to two, but not
spectacular at counting to ten. For this reason your computer represents numbers to base 2 rather than
base 10. This is called the
binary
system of counting, analogous to the
bi
cycle (two wheels). With the
decimal system, to base 10, the digits used can be from 0 to 9. In the binary system, to base 2, the digits
can only be 0 or 1, ideal when you only have on/off switches to represent them. Each digit in the binary
system is called a
bit
, being an abbreviation for
b
inary dig
it
. In an exact analogy to our usual base 10
counting, the binary number 1101 is therefore:
1 x 2 x 2 x 2 + 1 x 2 x 2 + 0 x 2 + 1
