Homework #4
January 19, 2011
1
Homework #4
due February 7 at noon
ECE 15a
Winter 2011
(2p) 1. Draw a Venn diagram illustrating the
operation.
2. Write the following functions using only + (OR),
(AND) and ’(NOT) operations:
(5p) (a) f = (a
b)(c
d)
(5p) (b) g= (a
b)
(c
d)
Simplify the expressions for f and g as much as you can.
3. A set of gates is said to be functionally complete (or universal) if and only if every Boolean function can
be realized entirely by means of gates from this set.
(a)(7p) Prove that the fgate defined as f(a,b,c) = a’c+b’c’+a’b is a universal gate. (Hint: Build
NOT, AND, OR gates using only the fgates)
(b) (6p) Build a 2input XNOR (equivalence) gate from the fgates defined above.
(3p) 4. Is it true that (a
b)(c
d)+a’b’d’+a’cd = a’b’c’d’+a’cd’+a’b’c+a’bd+b’cd’+ab’c’d ?
5. f(a,b,c,d) =
Σ
m(0,2,6,7,8,9,14,15)
(2p) Show a KMap for f(a,b,c,d).
(4p) List all prime implicants of f.
(4p) List all essential prime implicants of f.
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 Winter '08
 M
 Boolean Algebra, Karnaugh map, Canonical form, essential prime implicants

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