UC Davis
1
Hussain Al-Asaad
U
NIVERSITY
OF
C
ALIFORNIA
—D
AVIS
D
EPARTMENT
OF
E
LECTRICAL
& C
OMPUTER
E
NGINEERING
EEC180A—D
IGITAL
S
YSTEMS
I
Winter 2012
S
OLUTIONS
OF
P
RACTICE
P
ROBLEMS
— S
ET
1
1.
Draw the schematics of
in terms of AND, OR, and inverter gates.
2.
Draw the schematics of the following functions in terms of NAND and inverter gates.
3.
(a) Prove the simplification theorem
using the first eight laws of Boolean algebra (page 51
of textbook). There are several answers to this problem. Below is one of them.
=
Distributive law (8)
Distributive law (8)
Complementarity theorem (5D)
Operations with 0 (1)
Idempotent theorem (3D)
Commutative law (6D)
F
W X
YZ
+
=
W
X
Y
Z
F
X
Y
Z
a)
X YZ
XYZ
=
X
Y
Z
b)
XY
XZ
+
XY
XZ
+
XY
XZ
=
=
X
Y
+
X
Y
+
X
=
X
Y
+
X
Y
+
X X
Y
+
Y X
Y
+
+
XX
XY
YX
YY
+
+
+
XX
XY
YX
0
+
+
+
XX
XY
YX
+
+
X
XY
YX
+
+
X
XY
XY
+
+

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