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FA01-exam2-sol

# FA01-exam2-sol - UNIVERSITY OF CALIFORNIADAVIS DEPARTMENT...

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UC Davis 1 Hussain Al-Asaad U NIVERSITY OF C ALIFORNIA —D AVIS D EPARTMENT OF E LECTRICAL & C OMPUTER E NGINEERING EEC180A—D IGITAL S YSTEMS I F ALL 2001 M IDTERM II S TUDENT I NFORMATION I NSTRUCTIONS The exam is closed book and notes. Print your name and your ID number. Circle your lab section number(s). There are five problems in the exam. Solve all of them and show your work. If you need more space for your solution, use the back of the sheets. E XAM G RADE Name Hussain Al-Asaad ID Number xx-xxx-xxxx Lab Section Registered A01 (M 7-11pm) A02 (T 7-11pm) A03 (W 7-11pm) A04 (R 7-11pm) A05 (F 7-11pm) A06 (M 7-11am) A07 W 7-11am) Attending A01 (M 7-11pm) A02 (T 7-11pm) A03 (W 7-11pm) A04 (R 7-11pm) A05 (F 7-11pm) A07 (W 7-11am) None Problem Maximum Points Student Score 1 20 20 2 30 30 3 20 20 4 20 20 5 10 10 Total 100 100

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UC Davis 2 Hussain Al-Asaad 1. A RITHMETIC C IRCUITS (20 POINTS ) Design a gate-level circuit C that computes the function , where the input X is a 3- bit two’s complement number represented by X 2 X 1 X 0 and the output Y is a 5-bit two’s complement number represented by Y 4 Y 3 Y 2 Y 1 Y 0 . Minimize the number of gates in your design. Assume that the input combination X 2 X 1 X 0 = 100 will never appear at the inputs of C . Moreover, you can assume that the literals and their complements are available. The above solution requires four logic gates. In fact there exist a solution with three logic gates. This can be obtained by some logic manipulation of the Y 3 equation as follows: By using the above equation, we can implement the circuit C using three gates (two AND and one XOR). 2. F LIPFLOPS (10 + 10 + 10 = 30 POINTS ) In this problem, you are to analyze a new type of flip-flop, the XY flip-flop. The description of the XY flip-flop is given below.
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