Image Processing Reference
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XZ
 
2(2
nn
21
1)
Tx
 
2(
n
PT
)
(53)
1
Where
21
n
PH
 
2
TT

TTH

HH

(54)
21
n
10 2
n
10
2
n
2
n
1
Tv vvv
(55)

5
6
7
8 21
2
n
vx

xx
0 0

x
(56)

5
3,
n
1
3,1
3,0
3,
n

n
1
n
vK

KKK

KK

(57)
6
n
1
1
0
n
1
1
0
n
n
vx

xx
1 1

H
(58)

7
1,
n
1
1,1
1,0
2
n

n
1
n
vH


HH
(59)
8
2
n
1
1
0
2
n
Therefore, two modulo adders needed to realize (46) and (50). Moreover, (55) can be
implemented using three CSAs with EAC followed by a CPA with EAC. Note that some of
the full adders (FAs) of these CPAs and CSAs are simplified to XOR/AND or XNOR/OR
pairs due to the constant bits of the inputs. The final result, i.e. (53) can be obtained by a
(4 n +1)-bit binaryadder with '1' carry-in. Fig. 3 presents the reverse converter for the moduli
set {2 n -1, 2 n , 2 n +1, 2 2n +1 -1}.
6. Reverse converter for the moduli set {2 n -1, 2 n +1, 2 2 n , 2 2 n +1 -1}
The moduli set {2 n -1, 2 n , 2 n +1, 2 2n +1 -1} reduces the total delay of RNS arithmetic unit versus the
moduli sets {2 n -1, 2 n , 2 n +1, 2 2n +1} and {2 n -1, 2 n +1, 2 2n , 2 2n +1}. However, still the inter-channel
delay of modulo 2 2n +1 -1 is larger than the other three moduli, i.e. 2 n -1, 2 n and 2 n +1. Due to this,
the moduli set {2 n -1, 2 n +1, 2 2 n , 2 2 n +1 -1} has been recently proposed by (Molahosseini & Navi,
2010). The main advantage of this set is that it provides all of the merits of the moduli set {2 n -1,
2 n , 2 n +1, 2 2n +1 -1} while providing larger dynamic range (6 n -bit). Because, enhancing modulo 2 n
to 2 2 n is not increasing the complexity of the reverse converter.
The converter of (Molahosseini & Navi, 2010) has a two-level architecutre. In other words,
they have used a combinatorial conversion algorithm; consisting both CRT and MRC. First,
the previous CRT-Based design of reverse converter for the subset {2 2 n , 2 n -1, 2 n +1} (Hiasat &
Sweidan, 2004) is used to achieve the weighted equivalent of the residues ( x 1 , x 2 , x 3 ) as below
Zx

2
2
n
Y
(60)
1
Where
Yvvvv

(61)
1
2
3
4 21
2
n
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