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Student ID:. Name:. Computer Architecture and Organizat

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Student ID:Name:Computer Architecture andOrganization ICMPE 263Spring 2018March 2018Dept. of Computer Science andEngineeringCollege of EngineeringQatar UniversityHomework #1 – Spring 2018Digital Logic Circuit and Data RepresentationQuestion #1(4 marks):Given the Boolean function:F(A,B,C,D)=m(0,2,3,5,7,8,10,11,13,15)1)[2 marks]Drive the simplified Boolean function in sum-of-products form bymeans of a four-variable Karnaugh map.2)Draw the logic diagram witha.[1 mark]AND-OR gates;b.[1 mark]NAND gates.Question #1Solution 1):Boolean Function from K-mapCD00 01 11 10AB00011110The Boolean expression isF = BD + CD + B’D’Solution 2): a) BDD FCB’D’Page1of1250101101100110111
Student ID:Name:Solution 2): b) F= BD + CD + B’D’=́BD+CD+BD=́́BD.́CD.́B'D'BDC FDBDQuestion #2(2 marks):Given a JK flip flop, show how can you convert it into a D flip-flop.Solution Truth Table Of D Flip-flopINPUTOUTPUTSPRESENTSTATENEXTSTATEDQnQn+1000010101111JK to D Conversion TableExcitation Table of JK Flip-FlopPage2of12DINPUTOUTPUTSJKINPUTSPRESENTSTATENEXTSTATEDQnQn+1JK0000X010X11011X111X0OUTPUTSJKINPUTSPRESENTSTATENEXTSTATEQnQn+1JK000X011X10X111X0
Student ID:Name:DQn0 101J=DDQn0 101K=́DDJ Q QCLKCLKḰQ́QQuestion #3(6 mark):Design a priority encoder with three inputs X, Y, Z and three outputs A, B, C. Thetruth table for the circuit is shown below.a)[3 marks]Drive the minimized logic equations for A, B, and C (use Karnaughmaps).b)[3 marks]Draw the logic circuit diagram for A, B, and C.X Y ZA B C0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 10 0 00 0 10 1 10 1 11 0 11 0 11 0 11 0 1Page3of1200X112X3X011X203
Student ID:Name:Solution 3: a) Expression for AX YZ 00 01 11 1001A=XXAb)Expression for BX YZ 00 01 11 1001B=́XÝXBYc)Expression for CX YZ 00 01 11 1001C= X + Z + YXYCZQuestion #4(6 mark):Given a sequential circuit (shown in the figure below) that has two D flip-flopsAandB, two inputsXandY, and one outputZ.a)[2 marks]Write the logic function for the flip-flops inputsDAandDB, as afunction ofX,Y,AandB.b)[1 mark]Write the logic function for the outputZ.c)[3 marks]If thepresent stateofAandBareA = 1andB = 0, and the circuitinputs areX = 0andY = 0.Page4of12000011110011000001111111
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