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110年 - 110 國立臺灣大學_碩士班招生考試_電子工程研究所丁組:邏輯設計#101259
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題組內容
Problem 1: (20 points)
(e)(4%) Can any Boolean function be represented in the exclusive-product-of-suns (EPOS) expression, which is the XOR-AND two-level expression (with first level XOR and second level AND)? Justify your answer.
相關申論題
(a) (10%) Prove by induction that it represents an odd-parity function, that is, it evaluates to 1 if and only if the assignment to variables X1,...,Xn contains an odd number of 1's. (For example, the assignment (X1, X2, X3, X4)= (1,0,0,0) contains one 1.)
#424687
(b) (5%) How many product terms are there for its minimum sum-of-products (SOP) expression?
#424688
(c) (5%) How many sum terms are there for its minimum product-of-sums (POS) expression?
#424689
(a) (5%) Determine the minimum clock cycle that the circuit can operate.
#424690
(b) (5%) Determine the constraint on the flip-flop hold time for the circuit to operate correctly.
#424691
(c) (5%) Assume the combinational part of the circuit is to be re-implemented by a single read-only memory (ROM). Determine the size of the ROM in terms of 1) the number of words and 2) the bit-width of each word.
#424692
(d) (5%) Assume the circuit is initially in state (A,B,C,D) = (0,0,0,0). Determine the corresponding state-transition sequence and output sequence with respect to the input sequence 0, 1, 1.
#424693
(a) (10%) Draw the corresponding state graph and identify all equivalent states, if there is any, for state minimization.
#424694
(b) (10%) Implement the circuit with three D flip-lops and one majority gate MAJ.
#424695
(a)(5%) Find all possible initial state pairs between M1 and M2 that make the two circuits behave the same.
#424696
相關試卷
110年 - 110 國立臺灣大學_碩士班招生考試_電子工程研究所丁組:邏輯設計#101259
110年 · #101259
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