old_final_questions

old_final_questions - 1[30 points Short Questions 1.a Prove...

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1. [30 points] Short Questions 1.a. Prove or disprove that the operators ( ,XOR) form a complete set. Remember that the operator ( ) is implication such that: A B A B 0 0 1 0 1 1 1 0 0 1 1 1 1.b. Realize a 5-input NOR function using 2-input NOR gates only. 1.c. Implement the function F(A,B,C) = Σ m(1,2,4,5,7) using a 4:1 multiplexer (you also have GND and +5V available). 1.d. Implement both the two-input NAND and two-input NOR functions together using a single 2-to-4 decoder and a minimal number of additional OR gates. 1.e. Given that AB = 0 and A + B = 1, prove: AC + A’B + BC = B + C 1.f. Implement the following three functions using a PLA with two AND gates and 3 OR gates (show the PLA logic) F(A,B,C) = ABC ’ + ABC G(A,B,C) = A’BC + A’C H(A,B,C) = A’B’C + BC + ABC’ 2. [20 points] A reset-dominate latch has a set (L) and a reset (M) input. It differs from a conventional RS latch in that an attempt to simultaneously set and reset the latch (i.e., when L=1 and M=1) results in setting the latch so that it stores a 1. In a normal RS latch these would be forbidden inputs. 2.a. Derive the excitation table for this latch. REMEMBER: L = set and M = reset! 2.b. Derive the characteristic equation for this latch. 2.c. Show a logic diagram of this LM latch using only NOR gates and one 2-input AND gate if needed.

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3. [30 points] Short Questions 3.a. Demonstrate de Morgan’s theorem for
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old_final_questions - 1[30 points Short Questions 1.a Prove...

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