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# Fall 2002 - E CE290 Fall 2002 University o f Illinois HOUR...

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ECE290 University of Illinois Fall 2002 HOUR EXAM I Thursday, October 10, 2002 7-8:1Spm Closed Book. You are allowed one 8.5 x 11 inch sheet of notes. No calculators. No headphones. This exam contains 8 pages. Write your answers on these pages. Show all your work. If your work is not shown, you risk receiving no credit. Use backs of pages for scratch work if needed. The questions are not weighted equally. Budget your time accordingly. If you feel that a question is ambiguous, give your reasons and state your assumptions. PRINT NAME: SIGNATURE: Indicate your section: l. (11%) ( ) Bl Th 8 Kevin Squire 2. (9%) ( ) B2 Th 9 Kevin Squire 3. (10%) ( ) B3 Th 10 Tom Novak 4. (8%) ) B4 Th 11 Tom Novak 5. (8%) ( ) B5 Th 12 Frank Amoroso 6. (14%) 86 Th Matt McClain 7. (16%) ( ) B7 Th 2 Tom Soong 8. (14%) ) 88 Th 3 Siddhartha Bhatt 9. (10%) I Tctru . (100%) .I /' .

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Problem 1. (11 %) Boolean algebra. Each part is independent. (a) Give the exact dual of the following boolean expression. Do not simplify. a + b (c'd + e) 0 dual: (b) Express the following in minimal SOP form: ( w + i) ( V Y + Y v) (x + z W x) (y + z) minimal SOP: (c) Express the following in minimal pas form: ACE + CA (D 8 + 8 D) E minimal pos: ·1l+O.1l 's ... i;';T Dall··'I·.·.;.O II + • '"' .ldeiDpGieaCe 1 • II 'll + .' '" 1 ' 'rompkmeDtarlti7"j iii ;'0' ~(:I')' t:J ..•. 'ID~oiuriOD '" . _., . II + ''''Y + 1 " ,,' ~ commutadn" '1' =y'i' " ..' :1 + (y+' z) .;. (I + y)' +z' "'_lSdn .-- ·.ey"l) = (~ .. ')~ .. _ :ii '(y' •. ~>' ';'IlY + .1'·" .. r' itiSirlbild;Je .' 'X' ';,i = (I + y)(1 + ~) 1ts + yji'o::,ry,' _.;. -CleM.' ' :(IlJ)'';' ji + y' - ._ ,~, __ ", ,_.. . , .... f--'--'~--' ....... ".- ,.'--.-'.~ .. '''- , .......... . :1 + Iy = 1 : abiorptiOD :1 (I + y) •• · ... :.:ii"·,;;u·y .. ,. ··"ODUDeli .. -;SCI' +'y)',;,., ,. 'sy +1%+ Ilia 0:., +.~.ii;." .~oa..leII~~.:,j~I·+.Y?<! ~- z)(.' +'i) = (:I: Y)(~',+z) 2
---- Problem 2. (9%) Let v, w, x, y, z be elements in a boolean algebra. Circle T (true) or F (false) for each statement. Wrong answers will receive negative scores: a correct answer gets +3 points, a blank answer gets o

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