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practice q1

# practice q1 - CPRE 281 Practice questions for exam#1 1 Give...

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CPRE 281 -- Practice questions for exam #1 9/24/07 1. Give a truth table for each of the following logic expressions: (a) (X+Y)(X’+Y) (b) XY’+YZ’+ZX’ 2. For each of the expression in question 1, draw the circuit using the logic gate symbols. 3. For the logic expression in question 1 (a), (a) derive the canonical sum-of-products expression. (b) derive the canonical product-of-sums expression. 4. A 2-variable comparator circuit receives four input signals P1, P0, Q1, Q0 and produces an output signal F. The output F is 1 if either (i) P1>Q1 or (ii) P1=Q1 and P0 > Q0. (a) Write the truth table for the output function F. (b) Write the canonical SOP expression for F. Do not use shorthand notation. (c) Write the canonical SOP expression for F in shorthand notation. (d) Write the canonical POS expression for F. Do not use shorthand notation. (e) Write the canonical POS expression for F in shorthand notation. (f) Write the simplest logic expression for F by the Karnaugh map using SOP form. (g) Write the simplest logic expression for F by the Karnaugh map using POS form. (h) Let the cost of an expression be the total number of gates plus the total number of inputs of the circuit implementing the expression. Assume that AND gates and OR gates of any number of inputs are used in the implementation. NOT gates to complement the input variables are also counted. What is the cost of the expressions in (f) and (g)?

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