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Table 2.
Comparison of logic behavior and logic performance between NML and the
STT-based logic-in-memory architecture.
Nanomagnetic logic Logic-in-memory architecture
Logic characteristics and signal types
Cell types
Single layer nanomagnets
Multi-layer magnetic tunnel
junctions [
24
]
50 nm
2
,20nm[
32
]
50 nm
2
,20nm[
29
]
Cell dimensions
& spacing
100
×
100
×
Computing style
Dipolar magnetic coupling [
6
]
Dipolar magnetic coupling [
29
]
CMOS interface
None
Access transistors and metal
lines
User control
Over groups of cells
Over single MTJ with access
transistor [
24
]
Inputs
Oersted field or through explicit
neighbor interaction [
33
]
Electric, STT current [
24
]
Clock
Oersted field [
34
]
STT current [
30
]
Outputs
Magnetic sensing [
34
]
MR based [
24
]
Current
&
timing
Input current
(writing 1)
>
2
.
29 mA, 3 ns [
5
,
34
]
280
µ
A,
<
0
.
5ns [
24
,
35
]
Input current
(writing 0)
>
2
.
29 mA, 3 ns [
5
,
34
]
216
µ
A,
<
0
.
5ns [
24
,
35
]
Clocking current
2
.
29 mA, 3 ns [
34
]
170
µ
A, 3 ns [
30
,
35
]
Output current
−
30
µ
A, 4 ns [
24
]
As a quick recap, Shannon expansion allows any logic function
f
(
x
1
,x
2
,...,
x
i
,...,x
n
) to be expanded in terms of singled out variables
x
i
and their cofactor
f
i
as shown in Eq.
8
.
f
(
x
1
,x
2
,...,x
i
,...,x
n
)=
x
i
f
i
(
x
1
,x
2
,...,
1
,...,x
n
)+
x
i
ₓ
f
i
ₓ
(
x
1
,x
2
,...,
0
,...,x
n
)
(8)
Instead of computing the entire logic, we will now compute the cofactors in
the magnetic plane. The responsibility for the singled out variable(s) is trans-
ferred to the CMOS plane. For better understanding, let us once again look
into the 2-input exclusive-OR function. It can be readily expressed into singled
out variable
x
i
and cofactors
x
1
⊕ x
2
=
x
1
· x
ₓ
2
+
x
ₓ
1
· x
2
. Assuming the singled
out variable is
x
1
, our approach would require us to compute (
x
2
or
x
ₓ
2
)inthe
magnetic plane. This is much simpler. The final choice between
x
2
or
x
ₓ
2
in the
final output is now made in the CMOS plane depending on the value of
x
1
.
This approach significantly cuts down the cost of execution by avoiding some
intermediary logic steps in the magnetic plane. At the same time, it also retains
the flavor of non-volatile outputs. Some intermediary results are still left in the
magnetic plane.
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