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ECE15Amid1

ECE15Amid1 - TEST#1 Section A ECE 15a Winter 2008 l A...

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Unformatted text preview: TEST #1 Section A ECE 15a Winter 2008. l. A combinational circuit realizing function f is shown in the ﬁgure below. (4p) (a) Write an algebraic expression for f (4p) (b) Simplify f knowing that that the input combination (x,y,z)=(l ,l,0) never occurs. Draw the simpliﬁed circuit. The original and simpliﬁed circuit should produce the same output values on those input combination which may occur. I: (X H392 +Cx'32')']' = CCX+\3')7_]'X'«97_’ :- C(x+g')’+2"]x"3. 2': (XI? +L‘)K't9_2,’ : x'ta,2'+x'xaz' :x’ng' TEST #1 February 11, 2008 1 (5p) 2. Prove, that if A, B, C are Boolean variables for which both the conditions AB=AC and A+B=A+C hold, then it follows that B=C. TEST #1 February 11, 2008 2 3. F’(a,b,c,d) = Zm(0,1, 5, 7, 9, ll, 13). “ (a) Write the minterrn expansion for F(a,b,c,d) (1) (2p) in decimal form (ii) (31)) in algebraic form F: m’b’cd' + w'lo’cd 1— G—‘ke'ol' 4— «9’1”, 0“ +wb'e'ol'+ wb’cd' +a,bc«'d‘ +a—beol' wat‘?‘ (b) Write the maxterm expansion for F(a,b,c,d) (i) (2p) in decimal form F(&,\$)L)d) CTFCO;')‘;I-'FI3)H)|3) (ii) (3p) in algebraic form P(&_'(O)(Jd) 3 (“Li—4Q: he+d>C¢Ll—AO+C,+-d' )(n. '4'ng +d’). ~ C a. +&' +—c/' +d‘)(¢' 4—6 +0 FdDCup’FQl—L'Fd')Cm‘4~6(+—C+dl) TEST #1 February 11, 2008 3 \9 4. Given f(a,b,c,d) = ab’d’+a’c’d+bc’d’+a’b’d’+acd+bcd (5p) a. List all prime implicants of f. (3p) b. List all essential prime implicants of f. do“) Q‘o' Edd. (4p) c. Determine the minimum-literal sum—of—product representation of f. l _ [o’i'+o'd'+ 'C/I‘F (9— Ibd +~acol ' o 0' or- ACd4. mod «96 1900‘ 4- «Lb/C. TEST #1 February 11, 2008 5. Simplify the following Boolean function together with don’t cares: F(a,b,c,d)=Zm(0, 2, 8, 12) d(a,b,C,d):Zm(l,3,5,9,10,14,15) (5p) (a) Into minimum—literal Sum-of—Product (SOP) form, TEST #1 February 11, 2008 ...
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ECE15Amid1 - TEST#1 Section A ECE 15a Winter 2008 l A...

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