1.
(15%) Use QuineMcClusey Method to simplify the following canonical SOP forms. Identify
all Essential Prime Implicants based on the QM Method.
F
(
W
,
X
,
Y
,
Z
)
=
m
(0,3,4,5,7,9,11)
+
d
(8,12,13,14
∑
)
F
(
A
,
B
,
C
,
D
,
E
)
=
m
(0,4,12,15,27,29,30)
+
d
(1,5,9,10,14,16,20,28,31
∑
)
2.
(15%) Implement the following Boolean Expressions using Mixed Logic. For each equation,
show
two
implementations of the logic circuits  one completely in NAND gates and the
other completely in NOR gates. Write down how many NAND (or NOR) gates are needed
for each logic circuit.
Note
: Do not simplify the equations.
F
(
A
,
B
,
C
,
D
)
=
A
⋅
B
⋅
C
+
D
F
(
W
,
X
,
Y
,
Z
)
=
W
+
X
⋅
Y
+
Z
⋅
W
3. (15%)
Timing Diagrams:
Using the input waveforms below, sketch the outputs described in
each part below. Show the inputs as well as the outputs in each case so that it is clear where
each transition occurs.
a. Sketch the output F
2
= AB + AC + BC using the input waveforms A, B, and C shown
below.
b. If A, B, C, and D are the input lines to a 4 x 1 multiplexer (A = input 0), and S1, S0 are
the select lines, sketch the output Y.
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 Spring '09
 many
 Binarycoded decimal, 4bit BCD, sketch outputs D0, following canonical SOP, 4bit BCD number, 4bit BCD numbers

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