HW4_solution - ECE 2504 Introduction to Computer...

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1 ECE 2504 Introduction to Computer Engineering, Fall 2009 Homework 4 Due date: 22 Sep 09, 11:55pm Show all work. Use Logicworks to draw any circuit diagrams. 1. (6 pts) Simplify the following Boolean expressions. Provide the number of the Boolean identity used from Table 1-1 for each step. a. (BC ) (A C) (A B ) (B +C) (A+C ) (A B ) (16) (xy)’ = x’+y’ (B +C) (AA B + A B C ) (13) x(y+z) = xy + xz (B +C) (0•B + A B C ) (8) x•x’ = 0 (B +C) (0+ A B C ) (2) x•0 = 0 (B +C) (A B C ) (1) x+0 = x A B B C + A B CC (13) x(y+z) = xy + xz A B C + 0 (6) x•x = x; (8) x•x’ = 0 A B C (1) x+0 = x b. z (x + z) + xyz xz + z z + xyz (13) x(y+z) = xy + xz xz + 0 + xyz (8) x•x’ = 0 xz + xyz (1) x+0 = x xz (1 + y) (13) x(y+z) = xy + xz xz (1) (3) x+1 = 1 xz (4) x•1 = x c. y+x'y+w(w'+z') y•1+x'y+w(w'+z') (4)x•1 = x y(1+x')+w(w'+z') (14) x(y+z) = xy + xz y(1)+w(w'+z') (3) x+1 = 1 y+ww'+wz' (4) x•1 = x; (14) x(y+z) = xy + xz y+0+wz' (8) x•x’ = 0 y+wz' (1) x+0 = x
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2 2. (10 pts) Given the Boolean function F = xy z + x y z + x y z + x yz a. List the truth table. b. Draw the logic diagram using the original Boolean expression.
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HW4_solution - ECE 2504 Introduction to Computer...

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