EE 231 Fall 2007
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Homework #1 Due September 5, 2007
2.6 Use Venn diagram to prove that
21321321
)()(
xxxxxxxx
+=++•++
2.8 Draw a timing diagram for the circuit in Fig. 2.19a. Show the waveforms that can be
observed on all wires in the circuit.
2.11 Use algebraic manipulation to show that the three input variables x1, x2, and x3
∏
=
321
)6,5,4,3,2,1,0(
xxxM
2.12 Use algebraic manipulation to find the minimum sum-of-products expression for the
function
3213212131
xxxxxxxxxxf
+++=
2.21 Design the simplest sum-of-products circuit that implements the function
∑
=
).7,6,4,3,1(),,(
321
mxxxf
2.29 Design the simplest circuit that has 3 inputs, x1, x2, x3, which produces an output
value of 1 whenever exactly one or two of the input variables have the value 1; otherwise,
the output has to be 0.
2.34 For the timing diagram in Fig. P2.4, synthesize the function f(x1,x2,x3) in the
simplest POS form.
f
Fig. 2.19(a) A minimal sum-of-products realization
x1
x2
x3
