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Algorithm 2.
2-Input xor execution
x
1
⊕ x
2
with logic partitioning
1:
Input:
x
1
,
x
2
.
Output:
X
3
=
f
(
x
1
,x
2
)=
x
1
⊕ x
2
.
2:
Desired:
f
(0
,x
2
)=
x
2
;
f
(1
,x
2
)=
x
◦
2
.
3:
Logic execution sequence:
4:
Phase I:
Write X
1
=
x
2
and
X
2
=
x
◦
2
.
5:
Phase II:
Clock cell
X
3
6:
if
A
=1
then
7:
Clock cell X
1
8:
else
9:
Clock cell X
2
.
10:
end if
11:
Phase III:
Release the clock for cell
X
3
.
12:
Phase IV:
Deactivate all metal lines.
13:
14:
Cell Count N
=3.
15:
Total De lay T
=
t
w
+
t
clk
,where
t
w
and
t
clk
are the durations writing and
clocking cycles for a cell.
16:
Total Energy E
=
V
dd
×
(2
I
w
t
w
+2
I
clk
t
c
)
lk
,where
I
w
and
I
clk
are the average
currents to write and clock a cell.
for the MTJs. 2
I
w
t
w
V
dd
is the energy to write into
X
1
and
X
2
, while 2
I
clk
t
clk
V
dd
is the energy to clock cells
X
1
and
X
3
or
X
2
and
X
3
depending on the input.
Compare this to the standard mode of operation where the energy required
is (4
I
w
t
w
+9
I
clk
t
clk
)
V
dd
.4
I
w
t
w
V
dd
is the energy to write into the four cells
X
1
···X
4
(Fig.
6
) and 9
I
clk
t
clk
V
dd
is the energy to clock the nine cells
X
5
···X
13
in the body of logic. Logic partitioning therefore gives us an energy reduction
by (2
I
w
t
w
+7
I
clk
t
clk
).
For an average write current of
I
w
= 250
µ
A and an average clocking current
I
clk
= 170
A and a conservative write time of 0.5 ns and clocking time of 3 ns,
the logic partitioning provides a 48 % improvement in speed, over 65 % savings in
µ
Fig. 9.
Energy savings with STT-based logic-in-memory mode and logic partitioning
mode over traditional NML.
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