1. a) Label the inputs so that the output is
a.c
(a AND c)
b)
Using only AND, OR, NOT gates, draw the combinational logic network for
h which
precisely
corresponds to the following expression. Use fanout as
appropriate, but
do not simplify
.
h(w,x,y,z) = (w + x' + y) + 0 y' + (x' z + w')'
Assume that complemented inputs are available; i.e., assume that for each
variable w, x, y, z, both the variable and its complement are available as inputs:
w, w', x, x', y, y', z, z'.
2. a)
Consider the following 3input
XOR
gate
z
a
b
c
Write the formula for
z
in terms of AND, OR, and NOT.
b)
If any ONE of
a, b
or
c
is inverted, what is the new
z
? Show that this new
z
remains the same irrespective of which input you choose to invert.
This
Boolean expression corresponds to the output of a different type of gate;
what is this gate called?
c)
What happens to z if they are all inverted at the same time?
3. a)
A literal is a variable in its true or complemented form.
Simplify the
following functions such that there are minimum total literals. Write the
Boolean identity
you are using at each step.
Use no more than 8 steps per
item.
i)
(, ,) (
)
(
)
(
)
f xyz
x y x y z x y z
±
±
±
±
±
ii)
(,,,)
f wx y
zx
x
y
y
y
wx
wx
± ± ± ± ±
iii)
f(A,B,C,D) = (AB + A’B’)(C’D’ + CD) + (AC)’
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f(X, Y, Z) = X+Y(Z+(X+Z)±)
b) (i)
Use less than 6 steps to prove:
a' + wam' + wm + v'wz = a' + w
(ii)
State and prove the dual of the theorem in part (i). Align the dual proof
next to the original, and list the properties in the middle. No credit will
be given if the proof is not aligned as specified.
4.
You have seen a two valued Boolean algebra in class, where A= {0, 1}.
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 Spring '13
 Lgranger
 Logic, Gate, Boolean Algebra, Logic gate, exclusive or, XOR gate

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