quiz1b-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 - Section B QUIZ #1 Monday, September 26, 2005 Name: 50 [OCH 0"; 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. Part Score 1. X+0=X 2. X-1=X 3. Xl+1=1 4. X-O=0 5. X+X 2X 6. X-X 2X 7. X+3E=1 8. xizo 9. Y 2X 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: - l7 17. X__l7 = Y + Y DeMorgan’s 18. XY+YZ+YZ=XY+YZ 19. X+Y(Y+Z)(Y+Z) =(X+Y)(Y+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) : Find a simplified boolean expression of the following. F(a,,b,c) = HM(1,3, 6) 62 +ac+ $33 Problem 2 (20 pts): CMOS Switch Networks: a. Implement the following expressions using nMOS and pMOS transistors. Do not assume that complemented inputs are available. F=E(E+E) b. For the pull—up network below, give the Boolean expression and draw the corresponding pull—down network. out Problem 3 (25 pts): Minterms, Maxterms, Product of Sums, and Sums of Products: F(a,b,c) = m + 3(5 +52) ‘ 1. Express F(a, b, c) as a simplified sum of products. F : a<§+c> 4 E: (g+c> :qg+qc+a~‘3+ac =17 F;Q+ac+az—: G: 2. Express F(a, b, c) as a product of sums. F :1 E +qc+aa ‘1 5(E+ZS(Q+C) 2m+abc+qkz+gc “He ’— __ "‘ ~ - K <__ %?5 COuJA “(.50 Le our: A P ~ (q+!a+c.>(q+é\+c> 6””le 4mm “fire k‘MaP QLOUC 3. xpress (a, b, c) as a sum of minterms. F: ZM(O(I(ZIL/z‘$—I7) 4. Express F (a, b, c) as a product of maxterms. ' F: TIM/d Problem 4 (20 pts): Mixed logic: 1. Write down the exression corresponding to the gate network. 4— 22 Hans/57W; F:Z(D+E§+AE 2. Show the gate network (in mixed—logic format) corresponding to the same function as above but implemented only With N AND gates and inverters. A , ~ ' g :1}ij . ¥ C 9D <—. 21 foetus/:73 1‘; E _ 3. Write down the transistor count for Part 1 and Part 2 above. 2 2, €4.ch Problem 5 (15 pts): Convert the following numbers: 38 25.5625 010101 0101.01 01011010 7c 7c decimal => decimal => binary => binary ==> binary => hexadecimal: hexadecimalz} [OOI/O l/OOI. /o/ o/// [/00 121 binary binary decimal decimal ' hexadecimal binary decimal ...
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