課程名稱︰數位系統設計
課程性質︰必修
課程教師︰歐陽明
開課學院：電機資訊
開課系所︰資訊工程
考試日期（年月日）︰2011/1/12
考試時限（分鐘）：180
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. (Reverse Engineering) What is the counter state diagram implied by the
figure below ? There are two inputs to this counter. A is asserted to enable
counting. D is used to changed count direction, that is, go through the
sequence in reverse order. (15%)
Figure :

2. (FSM design and optimization) Consider a 4-bit sequence-detecting finite
state machine. The machine has a single input X and output Z. The output
is asserted after each 4-bit input sequence if it consists of one of the
binary strings 0110 or 1010. The machine returns to the reset state after
each and every 4-bit sequence.
(a) Create a "state diagram" for this 4-bit sequence detector. (5%)
(b) Use "Implication Chart Method" to reduce the number of states. (5%)
(c) Use the RS flip-flops to design the machine. (10%)
3. You have learned 4 types of flip-flop, D, R-S, J-K and T this semester.
(a) Please implement one type of flip-flops (RS) using basic logic
gates and state their truth table. (You can use AND, OR, NOT, NAND,
XOR and XNOR) (10%)
(b) Please design a 4-bit simple ring counter using T flip-flop. (5%)
(c) Please design a 4-bit Johnson counter using R-S flip-flop. (5%)
4. Please design a counter which can count from 0 to 15 and display on a
seven-segment LED display. (You can use all kinds of logic gates and flip
flop) (15%)
Figure :

5. When you were doing your final program project (Reverse engineering, or
Forward Design), what is your project ? What is your role in your project ?
What is the most difficult part in your role and please describe it, then
how you have solved your problem ? (10%)
6. Semi-conductor theory. We say that TSMC has the industry leading 40 nm
semiconductor process technology.
(a) When the poly-silicon and diffusion width is reduced by a factor of
R, so are others. That is, the source-drain voltage, the length,
oxide thickness (T0) all scaled by R. Please answer what is the
Packing density (gates/area) ? Power/gate. gate delay (speed) in
terms of R. Explain with simple explanations using the simple
circuit theory (For instance, resistance, capacitance, and speed),
and make your own assumptions. (10%)
(b) What is Moors' Law ? If hardware chips can follow Moors's Law, can
sofrware programming productivity follow it ? Why or why not ? How
to match the speed of Moors' Law in modern digital system design ?
(Hint : software design vs. hardware design) (5%)
(c) Current research shows that Moors' Law may reach its limit in 10
years for CMOS technology. The solution may go to multiple CPU/GPUs
in one chip. What are the impacts for the students who majored in
computer science ? (5%)