私立中原大學八十九學年度博士班招生考試命題紙

所組別：電子工程學系 科目：數位系統 考試時間：6月14日第1節

注意：題目總共有 6 題。
計分方式：第 1 題 10 分。第 2、3、4、5、6 題每題 18 分。
　
1. Use six 2-input NOR gates to implement the following function: F = A(B+CD)+BC’. Assume that both the normal and complement inputs are available.

2. Minimize the states for the finite state machine (FSM) given in the following table. Tabulate the minimal-state FSM.
 

Present state

Next state

Output

x=0

x=1

x=0

x=1

a

f

e

0

0

b

d

c

0

0

c

f

b

0

0

d

g

a

1

0

e

d

c

0

0

f

f

b

1

1

g

g

h

0

1

h

g

a

1

0

3. If you have three T flip-flops and some basic logic gates like AND, OR, XOR, etc., design a counter that counts in the following sequence: 0,1,3,7,6,4 and repeat.

4. If you have a stack machine, write a program to compute the expression
X= (A+B*C)*(D+E*F). The instructions available for use are as follows:
PUSH M
POP M
ADD
MULTIPLY
Note that M is the memory address. For example, the instruction “PUSH A” is to push the data content in address A into the stack.

5. Simplify the following Boolean functions by means of five-variable Karnaugh map: A’B’CE’+A’B’C’D’+B’D’E’+B’CD’+CDE+BDE’.

6. How many 128*8 RAM chips are needed to provide a memory capacity of 1024 bytes? Draw the block diagram and label the connections clearly.

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