MCE 335 - Logic Circuits HW1 14.10.2014 1. Demonstrate by means of truth tables the validity of DeMorgan’s theorem for 3 variables. 2. Demonstrate by means of truth tables the validity of the second distributive law: X+YZ = (X+Y)(X+Z) 3. Use algebraic manipulation to prove that (A + C) · (A + B) · (B + C) = B · C 4. Simplify yhe following Boolean expressions to expressions containing a minimum number of literals: (a) (A + B + C) · (ABC) (b) ABD + ACD + BD (c) (A + B)(A + C)(ABC) 5. Using DeMorgan’s theorem, express the function F = ABC + AC + AB (a) with only OR and complement operations. (b) with only AND and complement operations. 6. Optimize the following Boolean functions by means of a three-variable map: P (a) F (X, Y, Z) = m(0, 2, 6, 7) P (b) F (X, Y, Z) = m(0, 1, 2, 4) P (c) F (X, Y, Z) = m(0, 2, 3, 4, 6) P (d) F (X, Y, Z) = m(0, 2, 3, 4, 5, 7) 7. Implement function H = XY + XZ using two three-state buffers and an inverter. 8. Construct an XOR gate by interconnecting two three-state buffers and two inverters. 1
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