课程名称︰数位系统与实验
课程性质︰必修
课程教师︰欧阳明
开课学院：电机资讯
开课系所︰资讯工程
考试日期（年月日）︰2014/6/19
考试时限（分钟）：180
是否需发放奖励金：是
（如未明确表示，则不予发放）
好读 : http://www.ptt.cc/bbs/NTU-Exam/M.1403591255.A.8A5.html
试题 :
1. (5%) Convert a D flip-flop to a J-K flip-flop by adding external NAND gates.
2. (15%) Given a new flip-flop composed of two NAND gates.
Figure : http://i.imgur.com/stH2PCI.png
(5%) (a) What restriction must be placed on S* and R* so that P will always
equal Q' (under steady-state conditions) ?
(5%) (b) Construct a next-state table and derive the characteristic
(next-state) equation for the flip-flop.
(5%) (c) Complete the above timing diagram for this flip-flop.
3. (10%) Given a circuit shown in Fig.1, we assume that the inverters have a
delay of 10 ns. Initially A = C = D = 1 and B = 0, and C changes to 0
at time 10 ns.
Fig.1 : http://i.imgur.com/tGOLwi6.png
(6%) (a) Draw a timing diagram and identify where the hazard occurs.
(4%) (b) Modify the circuit to eliminate the hazard.
4. (20%)
(10%) (a) Draw state transition diagram for a machine that recognizes the
pattern "10(110)*01" in the input string. Note that (110)* denotes
zero or more occurence of the pattern 110. So, both 1001 (zero
occurence) and 1011011011001 (three occurence) are patterns we are
looking for. For example :
Input : 0010 1001 0110 1101 1001 1001 0111
Output: 0000 0001 0000 0000 0001 0000 0000
(10%) (b) Implement the design by using D flip-flops.
5. (10%) Design a sequential circuit. It has two inputs A and B, and one output
Y. When the circuit sees a "101" on input A, Y will outputs the
complement of B for the next 16 cycles; otherwise, Y will be 0. The
circuit should ignore what A is receiving during these 16 cycles. Use
positive-edge-triggered D flip-flops and a 4-bit binary counter as
your building block, and below is an example patterns :
Input A: 0011 0010 0110 1001 0010 1010 1110 0111
Input B: 1011 0011 1000 1111 0000 1111 1000 0011
Output Y: 0000 0000 0000 0000 1111 0000 1111 0000
6. (10%) Given two T flip-flops, add some logic circuit to them to make a
counter repeating the sequence of 0, 3, 1, 2, 0, 3, 1, 2, 0...etc.
7. (10%) Figure : http://i.imgur.com/IpA9aYv.png
(5%) (a) Describe what is the function performed by the following
state-transition diagram.
(5%) (b) Can the circuit function be performed by a circuit with fewer
states ? If yes, draw the new diagram.
8. (10%) For the sequential circuit shown below
Figure : http://i.imgur.com/c6yQzps.png
(5%) (a) Find the next-state equation and transition table for each
flip-flop (Ra, Rb, Rc).
(5%) (b) Please construct a state table for the circuit.
9. (10%) For the following circuit, complete the timing diagram as far as you
can, even after you no longer know the input.
Figure : http://i.imgur.com/rh9XjEC.png
X : 0 1 1 0 1 0 1
A : 0
B : 0
C : 0
D : 0