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__Decimal Numbers__

In practice we use a number
system called decimal number system. In the decimal number system
there are 10 numbers that we use 0,1,2,3,4,5,6,7,8,9. Using this ten
numbers we can show any decimal value that we want to. Consider the
number 251, we can describe it as251= 2X(10^2)+5X(10^1)+1X(10^0) =(2X100)+(5X10)+10X1=200+50+1

So you can see that as we move from right to left in a number, for each position the power increases by one. Let us consider a few more examples

62= (6X10^2)+(2X10^0)=60+2

7821=7X(10^3)+8X(10^2)+2X(10^1)+(1X10^0)=7000+800=20+1.

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__Other number systems__

In
addition to the decimal number system there can be multiple different
types of number system depending on number of literals that we want
to use to describe a number.

In
the hexadecimal number system in addition to the then literals 0...9
we also use the literals a,b,c,d,e,f. For the decimal number system
this numbers correspond to a=10, b=11, c=12, d=13, e=14, f=15.

So
(f)16=(15)10

If
we want to convert a hexadecimal number to a decimal number, the
method we need to follow is this:-

Consider
and hexadecimal number (f2a)16
. Now let us
convert this number into a decimal number

aX16^0+2X16^1+fX16^2

Now
we know that a=10 and f=15. Hence the above equation becomes:

10X1+2X16+15X256=10+32+3840=3882.

Now
to convert 3882 back to its hexadecimal form this what we will do.

16)3882(242

__32__

68

__64__

42

__32__

10

Reminder
10=f

16)242(15

__240__

2

Reminder
2

16)15(0

__00__

15

reminder
15=f

so
the hexadecimal number become (f2a)16

In
this way we can create any number system that we want to. We can even
use an octadecimal number system by just increasing two more number,
we can denote them as g and h, where g=16 and h=17.

Computers
that we use today process the numbers as binary digits 0 or 1.

The
decimal 5 is expressed as 101. Similarly (7)10=(111)2

Suppose
there is a binary number 11001, this is how we find its decimal
value.

We
will move from right to left and keep increasing the power of 2 for
each position. So

11001=1X2^0+0X2^1+0X2^2+1X2^3+1X2^4=1+0+0+8+16=25.

(11001)2=(25)10

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