Image Processing Reference
In-Depth Information
Therefore, these six operands should be added using a modulo (2 4 n -1) multi-operand adder
which can be realised by four carry-save adders (CSAs) with end-around carry (EAC)
followed by a modulo (2 4 n -1) carry propagate adder (CPA) with EAC (Piestrak, 1994, 1995).
The hardware architecture of the resulted converter is shown in Fig. 1.
x
x
x
x
3
2
4
Operand Preparation Unit
4 n -bit CSA with EAC
4 n -bit CSA with EAC
4 n -bit CSA with EAC
4 n -bit CSA with EAC
4 n -bit CPA with EAC
x
Z

X
Fig. 1. The converter for moduli set {2 n -1, 2 n , 2 n +1, 2 2n +1} (Cao et al., 2003)
4. Reverse converter for the moduli set {2 n -1, 2 n +1, 2 2 n , 2 2n +1}
The moduli set {2 n -1, 2 n +1, 2 2n , 2 2n +1} has been recently introduced by (Molahosseini et al.,
2010) to provide large dyamic range (6 n -bit), and high-speed reverse converter. Similar to
(Cao et al., 2003), the New CRT-I has used to design converter but with different moduli
order, i.e. {2 2n , 2 2n +1, 2 n +1, 2 n -1}. Therefore, by letting P 1 =2 2n , P 2 =2 2n +1, P 3 =2 n +1 and P 4 =2 n -1,
and putting the multiplicative inverses in the New CRT-I formulas (11)-(14), we have the
following main conversion equation (Molahosseini et al., 2010).
2
n
2
n
1
2
n
2(
xx

)2
(2
 
1 (
xx
)
2
n
2
1
3
2
Xx

2
(34)
1
2
n
22
(2
n
1)(2
n
1)(
xx
)
4
3
4
n
21
Simplification of this equation can be done as follows
Xx

2
2
n
Z
(35)
1
Where
Zv v v v v

(36)
1
2
31
32
4 21
4
n
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