中原大學九十二學年度碩士班入學招生考試

1.	(10分) Convert the following numbers to decimal:
2.	(10分) The NAND gate is said to be a universal gate because any digital system can be implemented with NAND gates alone. Prove that NAND gate is a universal gate.
3.	(15分) Design a counter that counts pulses on line w and displays the count in the sequence: 0, 2, 1, 3, 0, 2, …. Use natural binary coding and two T flip-flops as memory elements.
4.	(15分) Draw the truth table of a 4-to-16 decoder. And, design a 4-to-16 decoder using five 2-to-4 decoders. Note that the graphical symbol and the corresponding truth table of a 2-to-4 decoder are given in the following figure.
5.	(15分) Derive the state table and the state diagram for the circuit given in the following figures
6.	(15分) What is a critical path in a digital circuit? What is a false path in a digital circuit? Explain the terms critical path and false path. And, give examples for illustration.
7.	(20分) Write a VHDL code that represents a D flip-flop with an asynchronous reset input. Use behavioral code, rather than structural code.
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