Image Processing Reference
In-Depth Information
The number of different values the coefficient can take is equal to the base, hence
for base-10, ten different values are possible ( 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ) and for base-
2, two values are possible ( 0 , 1 ) .
Eight bits together is called a byte. A byte is shown as a row of eight bits (having
values 0 or 1). The bit to the left is called the most-significant bit (MSB) and the bit
to the right the least-significant bit (LSB). Converting a byte into a decimal number
is done by inserting the coefficients into the following equation (the eight right-most
termsofEq. A.5 ):
Decimal number
2 7
2 6
2 5
2 4
2 3
2 2
2 1
2 0
= x 7 ·
+ x 6 ·
+ x 5 ·
+ x 4 ·
+ x 3 ·
+ x 2 ·
+ x 1 ·
+ x 0 ·
Decimal number
=
x 7 ·
128
+
x 6 ·
64
+
x 5 ·
32
+
x 4 ·
16
+
x 3 ·
8
+
x 2 ·
4
+
x 1 ·
2
+
x 0
Some example byte values:
Binary
Decimal
00000000
0
00000001
1
00000010
2
00000100
4
00000101
5
00001111
15
00010101
21
01010101
85
10000000
128
11111111
255
As can be seen a byte is defined to have values from 0 to 255 (256 values in total).
Sometimes bytes are also appended to create numbers larger than 255. A common
example is two bytes together that spans the values 0
65535 (2 16
=
65536 in total).
A.1
Conversion from Decimal to Binary
A simple routine exists for getting the binary representation of a decimal number.
Initially, the largest power of two that is less than the decimal number is found. If the
decimal number is 137, the largest power of two is 128 (2 7 ). This is then subtracted
from the original number and the corresponding bit is set. This is repeated until the
decimal number is reduced to zero. In our example, 137 is found to be a sum of
128, 8, and 1 and therefore the binary representation of 137 is 10001001. Another
example:
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