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Sum
c out
z k
z k 1
z 0
···
Binary input x
Binary input y
A/D
x 0
c in
S 0
x k 1
x k 2
2 K 2
x 0
y k 1
y k 2
y 0
z
x n 1
2 K 1
1
2 K 1 2 K 2
···
···
1
Y 0
S n 1
c in
X
Y
y n 1
Digital to analog
converter
Digital to analog
converter
C in
C out
Figure 9.2. Structure of a nanoscale spin-wave full adder.
9.2.3. Nanoscale Spin-Wave Multiplier
A k-input multiplier is a device that multiplies two k-bit input values and generates
a2k-bit product. A spin-wave multiplier consists of k nodes representing input x,
k nodes representing input y,2 i intermediate nodes, t, and one node for analog
value of the output, P. These nodes intercommunicate via the spin-wave bus, as
shown in Figure 9.3.
The multiplication is implemented as x number of times adding the value of y.
This process is performed in three steps. Similar to a spin-wave adder, both binary
input values are converted to analog using digital to analog converters:
First Step. First the receiving frequency of t 0 t N 1 (t nodes) is tuned on the
sending frequency of x nodes. Each x i node (which has a value 1) sends a
spin-wave on the bust with its assigned amplitude, 2 k , to implement the
digital to analog conversion. Therefore, all the t nodes receive the analog
value of x.
Second Step. In the next step, the receiving frequency of t nodes is tuned on
the sending frequency of y nodes. Step 1 is repeated for y and the analog
value of y is received by t nodes.
Third Step.Eacht node compares its index to value of x.Ifitsindexislessthan
x,thet node broadcasts a spin-wave with an amplitude equal to the value of y.
P 2k 1
P 2k
P 0
Intermediate
Nodes
···
Binary input x
Binary input y
N = 2 K
A/D
x 0
x k 1
x k 2
2 K 2
x 0
y k 1
y k 2
y 0
P 0
t N 1
t N 2
t 0
P
x k 1
2 K 2
···
1
···
2 K 1
···
1
2 K 1
1
P 2k 1
2
3
X
Y
P
y 0
Digital to analog
converter
Digital to analog
converter
y k 1
Figure 9.3. Structure of a nanoscale spin-wave multiplier.
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