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# hw3 - logic functions in Problem 4 6(4 points After...

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CSE2300W Homework 3 1. (15 points) Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions. Indicate (or list) the distinguished 1-cells in each map. a) F = Σ W,X,Y,Z (4, 5, 6, 11, 12, 13, 14, 15) b) F = Σ W,X,Y,Z (0, 1, 2, 5, 9, 10, 11, 12, ) c) F = Π A,B,C (1, 3, 5, 6, 7) 2. (15 points) Using Karnaugh maps, find the complete sum for the logic functions in Problem 1. 3. (15 points) Using Karnaugh maps, find a minimal product-of-sums expression for the logic functions in Problem 1. 4. (15 points) Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions. Indicate (or list) the distinguished 1-cells in each map. d) F = Σ A,B,C,D (4, 5, 8, 10, 13, 15) + d (0, 1, 7, 11) e) F = Σ A,B,C,D (0, 1, 2, 8, 11) + d (3, 9, 5, 14) f) F = Σ A,B,C,D (1, 5, 12, 13, 14) + d (7, 9, 15) 5. (15 points) Using Karnaugh maps, find a minimal product-of-sums expression for the
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Unformatted text preview: logic functions in Problem 4. 6. (4 points) After completing the design and fabrication of an SSI-based digital system, a designer finds that one more inverter is required. However, the only spare gates in the system are a 2-input OR, a 3-input AND, and a 2-input XNOR. How should the designer realize the inverter function without adding another IC? 7. (21 points) Given a sum-of-products expression, it is possible to write the 1s corresponding to each product term directly on a Karnaugh map without developing an explicit truth table or minterm list, and then proceed with the map-minimization procedure. In this way, find a minimal sum-of-products expression for each of the following logic functions. a) F = X ′ • Z + X • Y + X • Y ′ • Z b) F = W ′ • X • Z ′ + W • X • Y + W • Z c) F = (W+Z ′ ) • (W ′ +Y+Z) • (X+Y+Z)...
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