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In-Depth Information
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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