Image Processing Reference
In-Depth Information
A
Bits, Bytes and Binary Numbers
When working with images it is useful to know something about how data are stored
in the memory of the computer. Most values associated with images are closely
related to the internal representation of the numbers. The value of one pixel is often
stored as one byte for example.
The memory of the computer can basically be seen as an enormous amount of
switches that can either be turned on or off. Each switch is called a bit (binary digit)
and can therefore be assigned either the value 0 or the value 1. So if you just wanted
to store values of either 0 or 1 it would be perfectly fine. However, this is rarely the
case and bits are combined to represent other types of number.
The binary number system is also called a base-2 system, since the basic unit only
has two values. Our
normal
system is a base-10 system and is called the decimal
system. To understand the base-2 system better, let us first have a look at the base-
10 system. When you see the following two numbers, 137 and 209814, you should
actually think like this in terms of the base-10 system:
10
2
10
1
10
0
1
·
+
3
·
+
7
·
=
100
+
30
+
7
=
137
(A.1)
10
5
10
4
10
3
10
2
10
1
10
0
2
·
+
0
·
+
9
·
+
8
·
+
1
·
+
4
·
=
200000
+
0
+
9000
+
800
+
10
+
4
=
209814
(A.2)
To generalize the formula we have
10
n
10
n
−
1
10
2
10
1
10
0
···
x
n
·
+
x
n
−
1
·
+···+
x
2
·
+
x
1
·
+
x
0
·
(A.3)
The
x
values are the
coefficients
of the base-10 system and they define the fi-
nal decimal number. This formula is similar no matter what base you use. Below
the general formulas for calculating a decimal number for base-16 (hexadecimal
numbers) and base-2 (binary numbers) can be seen:
16
n
16
n
−
1
16
2
16
1
16
0
(A.4)
Base-16:
···
x
n
·
+
x
n
−
1
·
+···+
x
2
·
+
x
1
·
+
x
0
·
2
n
2
n
−
1
2
2
2
1
2
0
Base-2:
···
x
n
·
+
x
n
−
1
·
+···+
x
2
·
+
x
1
·
+
x
0
·
(A.5)
