EE 231 Fall 2007
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Homework #5 Due November 19, 2007
4.10 Derive a minimum-cost realization of the four variable function that is equal to 1 if
exactly tow or exactly three of its variables are equal to 1; otherwise it is equal to 0.
4.21 Find the minimum-cost circuit for the function f(x1,…,x4) = Σm(0,4,8,13,14,15).
Assume that the input variables are available in uncomplemented form only. (Hint: use
functional decomposition).
4.23 Use the tabular method discussed in section 4.9 to find a minimum cost SOP
realization for the function f(x1,…,x4) = Σm(0,2,4,5,7,8,9,15).
4.33 Consider the circuit in Figure P4.2, which implements functions f and g. What is
the cost of this circuit, assuming that the input variables are available in both true and
complemented forms? Redesign the circuit to implement the same functions, but at as
low a cost as possible. What is the cost of your circuit?
6.1 Show how the function f(w1,w2,w3) = Σm(0,2,3,4,5,7) can be implemented using a
3-to-8 binary decoder and an OR gate.
6.4 Repeat problem 6.3 for the function
2132
wwwwf
+=
.
6.7 Consider the function
31312
wwwwwf
++=
. Show how repeated application of
Shannon’s expansion can be used to derive the minterms of f.
Figure P4.2. Circuit for problem 4.33.
f
g
x
2
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4
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4
x
1
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3
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1
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3
x
2
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3
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4
x
1
x
3
x
4
x
2
x
1
x
1
x
4
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3
x
1
x
4
