Image Processing Reference
In-Depth Information
Where
kP
1
(12)
1
1
PPP
234
kPP
 
1
(13)
2
1
2
PP
34
kPPP
  
1
(14)
3
1
2
3
P
4
Moreover, New CRT-II (Wang, 2000; Molahosseini et al., 2010) provides a tree-like
architecture by using the following equations
XZPPkYZ

12 1 (
) PP
(15)
34
Zx Pkx x

(
) P
(16)
1
1
2
2
1
2
Yx Pkx x

(
) P
(17)
3
3
3
4
3
4
Where
kPP
1
(18)
112
PP
34
kP
1
(19)
21
P
2
kP
1
(20)
33
P
4
The New CRTs have potentiality to create higher performance reverse converters than CRT
and MRC particularly for some special four-moduli sets. Hence, many research have been
done in the recent years to discover efficient four-moduli sets which can be fitted with
properties of New CRTs. In the next sections, we investigate the reverse converters that are
previously designed for these four-moduli sets.
3. Reverse converter for the moduli set {2 n -1, 2 n , 2 n +1, 2 2n +1}
The moduli set {2 n -1, 2 n , 2 n +1, 2 2n +1} was introduced by (Cao et al., 2003). They have used
New CRT-I to design a fully adder-based reverse converter. In the following, we briefly
review the conversion formulas and hardware architecture of the converter of (Cao et al.,
2003). First, consider the moduli set {2 n -1, 2 n , 2 n +1, 2 2n +1} with corresponding residues ( x 1 ,
x 2 , x 3 , x 4 ). The residues can be represented in bit-level as below

(21)
xx x
(

xx
)
1
1,
n
1
1,
n
nbits
2
1,1
1,0
2
(22)
xx x
(


xx
)
2
2
2,
n
1
2,
n
nbits
2
2,1
2,0
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