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quiz1a-solutions

# quiz1a-solutions - GEORGIA INSTITUTE OF TECHNOLOGY School...

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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY School of Electrical and Computer Engineering ECE 2030 QUIZ #1 Monday, September 26, 2005 Name. Sol u‘l‘fo n5 Last, First 0 Closed book, closed notes. 0 None of the problems require involved calculations. Reconsider your approach before doing something tedious. 0 Clearly identify each answer. Total 100 1. X+0=X 2. X-1=X 3. X+1=1 4. X-0:0 5. X+X=X 6. X-X=X 7. X+X=1 8. X.Y=0 9. Y =X 10. X + Y = Y + X 11. XY = YX Commutative 12. X + (Y + Z): (X + Y) + Z 13. X(YZ) = (XY)Z Associative 14. X(Y+Z)=(XY+XZ) 15. X+YZ=(X+Y)(X+Z) Distributive 16. X+Y=X-? 17. X_-T7=X+T; DeMorgan’s 18. XY+XZ+YZ=XY+XZ 19. (X+Y(X+Z)(Y+Z) =(X+Y)(X+Z) Problem 1 (20 pts): Find the most simpliﬁed POS and SOP expressions for the K—map below. Show your work by Circling all the prime implicants corresponding to your answer. F1(a,b, c, d) : ___J nun Iran .4 [Ella Fm, b, c) = HM(1,3, 5) Problem 2 (20 pts): CMOS Switch Networks: a. Implement the following expressions using nMOS and pMOS transistors. Do not assume that complemented inputs are available. I F=EE+E b. For the pull-up network below, give the Boolean expression and draw the corresponding pull-down network. 81% b e d %E c4 out Problem 3 (25 pts): Minterms, Maxterms, Product of Sums, and Sums of Products: F(a,b,c) = (55 +c) + a(b+ bc) 1. Express F (a, b, c) as a simpliﬁed sum of products. F: (0+5); + 5(54—c3 :q€+b2+ab+ac_ =5 'ZF1aZ-l-x‘354-aci (:11 -~or._ F : a5 + a b + ac 2. Express F(a, b, c) as a pro uct 0 sums. 3. Express F (a, b, c) as a sum of minterms. Problem 4 (20 pts): Mixed logic: 1. Write down the exression corresponding to the gate network. L( Z ‘1 :DHP L 12 madam E—-{>O~ F = (Mm—c.) MM?) 2. Show the gate network (in mixed-logic format) corresponding to the same function as above but implemented only with NAND gates and inverters. —i> «if A B c. B E 22, +rw4\$ am 3. Write down the transistor count for Part 1 and Part 2 above. 22 €o..CL\ Problem 5 (15 pts): Convert the following numbers: 01101 011.01 38 25.3125 8a 8a 10110110 binary => binary :> decimal => decimal 2: hexadecimal: hexadecimal: binary => 3.25 0100110 (loo/.0101 IOOO LQLO 132 136 decimal decimal binary binary binary decimal hexadecimal ...
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