Web_Answers_9 - = B'C'D + AC → Use 2 AND gates 9.11 (b) F...

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Unit 9 Problem Solutions 9.1 See FLD p. 636 for solution. 9.2 See FLD p. 636 for solution. 9.3 See FLD p. 637 for solution. 9.4 See FLD p. 637 and Figure 4-4 on FLD p.99. 9.5 y 0 y 1 y 2 y 3 a b c 0 0 0 0 0 0 0 1 0 0 0 0 0 1 X 1 0 0 0 1 1 X X 1 0 1 0 1 X X X 1 1 1 1 y y y y 00 01 11 10 00 01 11 10 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 2 3 a = y + y 2 3 3 00 01 11 10 00 01 11 10 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 b = y + y ' y y y y y 0 1 2 3 1 2 3 0 00 01 11 10 00 01 11 10 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 c = y + y + y + y 2 1 y y y y 0 1 2 3 9.6 See FLD p. 638 for solution. See Errata at http://www.ece.utexas.edu/projects/ee316/Errata.pdf for correction. 9.7 See FLD p. 638 for solution. 9.8 See FLD p. 638-639 for solution. 9.9 The equations derived from Table 4-6 on FLD p. 101 are: D = x'y'b in + x'yb in ' + xy'b in ' + xyb in bout = x'b in + x'y + yb in See FLD p. 639 for PAL diagram. 9.10 Note: A 6 = A 4 ' and A 5 = A 4 . Equations for A 4 through A 0 can be found using Karnaugh maps. See FLD p. 640-641 for answers. 9.11 (a) F = C'D' + BC' + A'C → Use 3 AND gates F' = [C'D' + BC' + A'C]' = [C' (B +D') + CA']' = [(C + B + D') (A' + C')]'
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Unformatted text preview: = B'C'D + AC → Use 2 AND gates 9.11 (b) F = A'B' + C'D' → Use 2 AND gates F' = (A'B' + C'D')' = [(A' +C') (A' + D') (B' + C') (B' + D')]' = AC + AD +BC +BD → Use 4 AND gates 9.12 (a) See FLD p. 641, use the answer for 9.12 (b), but leave off all connections to 1 and 1'. 9.12 (b) See FLD p. 641 for solution. 9.13 B C D E A 1 00 01 11 10 00 01 11 10 1 1 1 1 1 1 1 B = 1 B = 0 Using Shannon’s expansion theorem: F = ab'cde' + bc'd'e + a'cd'e + ac'de' = b' (acde' + a'cd'e + ac'de') + b (c'd'e + a'cd'e + ac'de') = b' [ade' (c + c') + a'cd'e] + b [(c' + a'c) d'e + ac'de'] = b' (ade' + a'cd'e) + b (c'd'e + a'd'e + ac'de') The same result can be obtained by splitting a Karnaugh map, as shown to the right....
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This note was uploaded on 09/03/2008 for the course EE 316 taught by Professor Brown during the Fall '08 term at University of Texas at Austin.

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