Final-solutions - Faculty of Engineering ELECTRICAL AND...

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Faculty of Engineering ELECTRICAL AND ELECTRONIC ENGINEERING DEPARTMENT EENG115/INFE115 Introduction to Logic Design EENG211/INFE211 Digital Logic Design I Fall 2009-10 Instructors: M. K. Uyguro ğ lu H. Demirel Final EXAMINATION Jan. 13, 2010 Duration : 120 minutes Number of Problems: 8 Good Luck STUDENT’S NUMBER NAME SURNAME GROUP NO Problem Achieved Maximum 1 10 2 10 3 15 4 15 5 10 6 15 7 15 8 15 TOTAL 105
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Introduction to Logic Design/ Digital Logic Design I - Final Examination Question 1 (10 points) Answer the following questions regarding Boolean algebra. a) Minimize the function F(w,x,y,z) using algebraic modifications. Show the result as a sum of products with a minimum number of literals. (6 points) F(w,x,y,z) = (y’+wy’(xz+xz’))z + (xy’+(x+y)’+z’)’+ y(z+wx’(w’+z)) =[y` +wy`x]z + (xy` +x`y` + z`)` + y(z + wx`z) = y`z + wxy`z + ( y` + z` )` + y (z) = y`z ( 1 + wx) + yz + yz = y`z + yz = z Algebraically minimized F = z b) Convert the original function F(w,x,y,z) from part a) to a sum-of-product form and minimize it using Karnaugh map. Compare the results. (4 points) F(w,x,y,z) = (y’+wy’(xz+xz’))z + (xy’+(x+y)’+z’)’+ y(z+wx’(w’+z)) =[y` +wy`x]z + (xy` +x`y` + z`)` + y(z + wx`z) = y`z + wy`xz + yz + wx`yz K-map minimized F = _________________ 00 01 11 10 00 01 11 10 z 1 1 1 1 1 1 1 1 z M. K. Uyguro ğ lu, H. Demirel Jan. 13, 2010
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Introduction to Logic Design/ Digital Logic Design I - Final Examination Question 2 (10 points): Answer the following questions regarding combinational logic.
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Final-solutions - Faculty of Engineering ELECTRICAL AND...

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