Image Processing Reference
In-Depth Information
XZ
2(2
2
n
2
n
1)2
2
n
3
(
x Z
)
x
2(
2
n
Y
2
2
n
TT
)
(66)
4
1
21
n
2
1
Where
Tvvv
(67)
5
6
7
2
21
n
1
vx
xx x
0
(68)
5
1,2
n
2
1,1
1,0
1,2
n
1
21
n
vY
YY
0
(69)
6
2
n
1
1
0
2
n
vx
xxxx
(70)
7
4,2
n
2
4,1
4,0
4,2
n
4,2
n
1
21
n
The hardware implementation of this converter relies on two modulo adders for realization
of (61) and (67). In other words, (61) needed two 2
n
-bit CSAs with EAC and a 2
n
-bit CPA
with EAC, and a (2
n
+1)-bit CPA with EAC is used to realize (67). Besides, (66) only requires
one (4
n
+1)-bit regular binary adder; the required multiplications all can be done using shift
and concatenation. The converter has been depicted in Fig. 4.
7. Complexity comparison
Table 1 presents the total hardware requirements and conversion delays of the reverse
converters for the large dynamic range four-moduli sets in terms of logic gates and FAs.
Note that
A
FA
and
D
FA
indicate the area and delay of one FA, respectively. It can be seen that
the fastest converter is the converter for moduli set {2
n
-1, 2
n
+1, 2
2n
, 2
2n
+1}. Because, the
dynamic range of this set is 6
n
-bit while the dynamic range of moduli set {2
n
-1, 2
n
, 2
n
+1,
2
2n
+1} is 5
n
-bit. Therefore, for providing the same dynamic range, the value of
n
for the first
Moduli set
Hardware Requirements
Conversion Delay
(8
n
+2)A
FA
+ (
n
-1)A
XOR
+ (
n
-1)A
AND
+ (4
n
+1)A
XNOR
+(4
n
+1)A
OR
+ (7
n
+1)A
NOT
+ (
n
)A
MUX2×1
{2
n
-1, 2
n
, 2
n
+1, 2
2
n
+1
-1}
(12
n
+5)
D
FA
+3
D
NOT
+
D
MUX
(10
n
+3)A
FA
+ (
n
+1)A
XOR
+ (
n
+1)A
AND
+ (3
n
-1)A
XNOR
+(
3n
-1)A
OR
+ (7
n
+3)A
NOT
{2
n
-1, 2
n
+1, 2
2n
, 2
2n
+1
-1}
(12
n
+6)
D
FA
+2
D
NOT
(11
n
+6)A
FA
+ (2
n
-1)A
XOR
+ (2
n
-1)A
AND
+ (4
n
)A
XNOR
+(4
n
)A
OR
+ (5
n
+3)A
NOT
{2
n
-1,2
n
, 2
n
+1, 2
2
n
+1}
(8
n
+3)
D
FA
+
D
NOT
(10
n
+6)A
FA
+ (4
n
-3)A
XOR
+ (4
n
-3)A
AND
+ (2
n
-3)A
XNOR
+(2
n
-3)A
OR
+ (6
n
+3)A
NOT
{2
n
-1, 2
n
+1, 2
2
n
, 2
2
n
+1}
(8
n
+3)
D
FA
+
D
NOT
Table 1. Hardware requirements and conversion delays of the reverse converters for the
large dynamic range four-moduli sets