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：电资学院
开课系所︰资工系
考试日期（年月日）︰2015.06.25
考试时限（分钟）：
试题 :
Digital System Design and Lab, Final Exam 6/25/2015
1. (10%) Determine the Q output for the negative-edge-triggered J-K flip-flop
for the input waveform, and assume that Q=0 initially
┌─────┐ ┌────────
J │ │ │
0 ─────┘ └─────┘
┌──────────────
K │
0 ───────────┘
┌──┐ ┌──┐ ┌──┐ ┌──┐
CLK │ │ │ │ │ │ │ │
0 ──┘ └──┘ └──┘ └──┘ └──
Q
T_1 T_2 T_3 T_4 T_5 T_6 T_7 T_8
2. (10%) For the Moore machine state table given below, please determine a
minimal state table.
┌───────┬─────┬───┐
│Present state │Next state│Output│
├───────┼─────┼───┤
│ │ Input │ │
│ │ ０ １ │ │
├───────┼─────┼───┤
│ Ａ │ Ｂ Ｃ │ １ │
├───────┼─────┼───┤
│ Ｂ │ Ｄ Ｅ │ ０ │
├───────┼─────┼───┤
│ Ｃ │ Ａ Ｆ │ １ │
├───────┼─────┼───┤
│ Ｄ │ Ｅ Ｃ │ ０ │
├───────┼─────┼───┤
│ Ｅ │ Ｇ Ｈ │ １ │
├───────┼─────┼───┤
│ Ｆ │ Ｂ Ｈ │ １ │
├───────┼─────┼───┤
│ Ｇ │ Ｄ Ｆ │ ０ │
├───────┼─────┼───┤
│ Ｈ │ Ｆ Ｅ │ １ │
└───────┴─────┴───┘
3. (20%) Our TA wants to make a 0(010)*1 recognizer and gets a state diagram.
Given this state machine (see the following figure), please answer the
following questions.
(a) (3%) Is it a Moore machine or a Mealy machine?
(b) (3%) Draw the state transition table for this state diagram.
(c) (4%) Try to reduce the number of states first using Implication Chart
Method. What are the benefits of reducing states number of a machine?
(d) (10%) Implement a circuit of this machine using D flip-flop(s). Use as
few flip-flops as possible.
Figure: http://i.imgur.com/GeyhD9Y.png
4. (20%) (Reverse Engineering) Consider a sequential circuit shown in following
diagram. It has one input x. one output z with a clock trigger signal clk
(rising edge trigger for flip-flops).
(i) (10%) Draw the state transition diagram first.
(ii) (10%) Please draw the output waveform of z.
Figure01: http://i.imgur.com/Kg4YQVP.png
Figure02: http://i.imgur.com/Hutqu4I.png
5. (20%) Design a system (a counter) using four T flip flops, A, B, C, D. It
is a binary-coded-decimal, using 2421 code below, and is going through the
sequence: 0, 2, 6, 9, 3, 5, 8, 7, 4, 1.
┌───────┬─────┐
│Decimal digit │2421 code │
├───────┼─────┤
│ 0 │ 0000 │
├───────┼─────┤
│ 1 │ 0001 │
├───────┼─────┤
│ 2 │ 0010 │
├───────┼─────┤
│ 3 │ 0011 │
├───────┼─────┤
│ 4 │ 0100 │
├───────┼─────┤
│ 5 │ 1011 │
├───────┼─────┤
│ 6 │ 1100 │
├───────┼─────┤
│ 7 │ 1101 │
├───────┼─────┤
│ 8 │ 1110 │
├───────┼─────┤
│ 9 │ 1111 │
└───────┴─────┘
6. (20%) Design a sequential system (a counter) with one input line, x, and
three flip flops, A, B, C. When x = 0, the system sequences through the
state (0, 1, 2, 3, 4) repeatedly, and when x = 1, the system sequences
through (2, 3, 4, 5, 6, 7) repeatedly. If at any time, x is 0 when the
state is in states 5, 6, or 7, or if x = 1 when the system is in
states 0, or 1, it should go to state 3 on the next clock.
(i) (10%) Draw the state transition table for this machine.
(ii) (10%) Design the system using D flip flops.