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SP99-exam2-sol

# SP99-exam2-sol - LUNIVERSITY OF CALIFORNIADAVIS DEPARTMENT...

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UC Davis 1 Hussain Al-Asaad L U NIVERSITY OF C ALIFORNIA —D AVIS D EPARTMENT OF E LECTRICAL & C OMPUTER E NGINEERING EEC180A—D IGITAL S YSTEMS I S PRING 1999 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 xxx-xx-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 (W 7-11am) A07 (R 7-11am) Attending A01 (M 7-11pm) A02 (T 7-11pm) A03 (W 7-11pm) A04 (R 7-11pm) A05 (F 7-11pm) A06 (W 7-11am) A07 (R 7-11am) Problem Maximum Points Student Score 1 20 20 2 20 20 3 15 15 4 25 25 5 20 20 Total 100 100

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UC Davis 2 Hussain Al-Asaad 1. I MPLEMENTATION M ETHODS (5 + 5 + 5 + 5 = 20 POINTS ) In this problem, you are to design a 2-bit equality checker using several methods. The equality checker compares two unsigned 2-bit numbers A and B and produces and output E that is set to 1 if and only if the two numbers A and B are equal. 1.1 Complete the Karnaugh Map of the equality checker. 1.2 Implement the equality checker using an 8-to-1 multiplexer. Assume that the inputs and their complements are available. 1.3 Implement the equality checker using a 4-to-1 multiplexer and 2-input AND gates. Assume that the inputs and their complements are available. A 1 A 0 B 1 B 0 E { { A B Equality checker A 1 A 0 B 1 B 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 00 01 10 11 00 01 10 11 0 1 2 3 1 0 8-to-1 MUX 4 5 6 7 E 0 0 0 0 2 B 0 B 0 B 0 B 0 A 1 A 0 B 1 0 1 2 3 1 0 4-to-1 MUX A 1 A 0 B 0 B 1 E B 0 B 1 B 0 B 1 B 0 B 1
UC Davis 3 Hussain Al-Asaad 1.4 Implement the equality checker using a 4-to-1 multiplexer and a 2-to-4 decoder only.

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