The number of switching elements achievable in the
final answer is given for you.
(a) This circuit can be simplified down to 6 switching elements. (Note that 4
of the switching elements shown are for negated variables.)
a
X
X
X’
Y
W
S
Z
Z’
V
b
Z’
V
Z
W
S’
Z
Y
V
(b) This circuit can be simplified down to 6 switching elements. (Note that 4
of the switching elements shown are for negated variables.)
b
S
Y
X
Y’
V
W
S
Z
Y
S
Y
Z’
X’
S
V
a
X’
Y
S
W
(c) This circuit can be simplified down to 9 switching elements. (Note that 7
of the switching elements shown are for negated variables.)
Y
X
Y
W
S
V
V
V
Z
W
S
X
S
X
S
Y
W
Y
a
Z
S
V
S
b
V
Z
Z
Y
X
X
X
V

EE 5393, Winter ’13
3
(d) This circuit can be simplified down to 8 switching elements (7 for extra
credit).
(Note that 9 of the switching elements shown are for negated
variables.)
a
Z
X
Z
Y
X’
Z
V
Y’
X
S
V’
b
V’
S
Y’
S
Y
V’
S
Y
Y’
Z’
X
Z
S
Y
X
Y
Y
S’
Y
V
W
S
S

EE 5393, Winter ’13
4
2.
Two-Terminal Switches, but Multiple Circuit Terminals
(no collabora-
tion)
A generalization of the switching circuit model is a circuit with
multiple circuit
terminals.
A function
F
ab
is 1 if there is a closed path between terminals
a
and
b
, and 0 otherwise. With multiple circuit terminals,
a, b, c, d, . . .
, different
functions can be implement between
pairs
of terminals. For instance, for the
circuit
x
y'
z
a
b
e
c
x'
y
d
f
we have
F
af
=
xyz
F
bd
=
x
0
z
F
cf
=
0
.
and so on. For the circuit
w
x
y
z
a
b
c
we have
F
ab
=
x
+
w
F
bc
=
y
+
z
F
ac
=
(
x
+
w
)(
y
+
z
)
.
As these examples show, you can use either a variable or its complement to
control a switch. (Each terminal is, in fact, any stretch of wire.)

EE 5393, Winter ’13
5
(a) Construct a circuit with 3 switches that implements the functions
f
1
=
xy
f
2
=
x
0
y
(b) Construct a circuit with 4 switches that implements the functions
f
1
=
xy
+
x
0
y
0
f
2
=
x
0
y
+
xy
0
(c) Construct a circuit with 6 switches that implements the functions
f
1
=
x
(
y
+
z
)
f
2
=
y
(
x
+
z
)
f
3
=
z
(
x
+
y
)
f
4
=
x
+
yz
f
5
=
y
+
xz
f
6
=
z
+
xy
(d) Construct a circuit with as few switches as possible that implements all
functions of two variables.
A solution with 8 switches gets full credit.

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