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homework_4_ece15a_11 - Homework#4 due February 7 at noon...

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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 f-gate 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 f-gates) (b) (6p) Build a 2-input XNOR (equivalence) gate from the f-gates 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 K-Map 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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