課程名稱︰交換電路與邏輯設計
課程性質︰大二必修
課程教師︰簡韶逸
開課學院：電資學院
開課系所︰電機工程學系
考試日期（年月日）︰2014/11/14
考試時限（分鐘）： 110分鐘
試題 :
Switching Circuits & Logic Design, Fall 2014
Midterm Exam (3:30pm ~ 5:20pm, 2014/11/14)
Problem 1:(5%)
Let (1001)_R = (101)_3R. What is the number R ?
Problem 2:(20%)
There are five fruits F_1,F_2,F_3,F_4 and F_5, whose nutrients are listed
in the following table, where a "v" indicates the availability of some
vitamin in some fruit. (For example, fruit F_1 contains vitamins B,C,but
not vitamins A,D,E.)
表格如：http://ppt.cc/Ut40
(不太會畫，sorry)
(A)Please write a formula expressing the condition that which fruits one
has to get in order to obtain vitamin A.(5%)
(B)Pelease write a product-of-sums(POS) formula in terms of Boolean variables
F_1,F_2,F_3,F_4, and F_5 such that it is true for some { 0 , 1 }-assignment to the Boolean variables
if and only if all vitamins are obtained by the collection of fruits with
F_i = 1 in the assignment.(5%)
(C)Suppose we want to buy as few fruits as possible while obtaining all
vitamins. What fruits should we buy? How does this problem relate to the
minimized sum-of-products (SOP) expression of the formula in (B)? (10%)
Problem 3:(10%)
F and G are four-variable functions, where:
F(a,b,c,d) = ΠM(1,5,7,11,14,15) x ΠD(2,3,10)
G(a,b,c,d) = Σm(0,1,3,7,8,9,15) + Σd(10,11)
(A)What is the maxterm expansion of G(a,b,c,d) ? (5%)
(B)Provide the product of the two functions, FG(a,b,c,d), in the minterm
expansion. (5%)
Problem 4:(30%)
Please design a combinational circuits with four input pins, A, B, C and D.
(ABCD) is the BCD(Binary Coded Decimal) representation of a decimal digit,
where A is the MSB, and D is the LSB. The output F(A,B,C,D) has value 1 if
the decimal digit represented by A,B,C and D is divisible by either 3 or 4
(zero is divisible by 3 and 4).
(A) Draw the Karnaugh map for F. (4%)
(B) Find all minimum sum of products for F. Please mark all essential prime
implicants.(8%)
(C) Design the AND-OR circuit and OR-AND circuit with minimum gates.(10%)
(D) Design the two-level circuits with minimum and only NAND gates.(4%)
(E) Design the two-level circuits with minimum and only NOR gates.(4%)
Problem 5: Timing diagram(15%)
Consider the 4-bit full adder shown below. Each full adder has a propagation
delay of 1ns. (A_3,A_2,A_1,A_0) changes from (0,0,0,0) to (o,1,1,1) and
(B_3,B_2,B_1,B_0) changes from (0,0,0,0) to (1,1,0,1) at t=0, as shown below.
Complete the following timing diagram of C_4,S_3 and S_2 from t=1~5ns.
http://ppt.cc/tJUo
(4-bit full adder & timing diagram)
Problem 6:(20%)
Braille is a system which allows a blind person to read alphanumeric by
feeling a pattern of raised dots. Design a circuit that converts BCD
(Binary Coded Decimal) to Braille. The table1, shows the correspondence
between BCD and Braille.
http://ppt.cc/5zFK
(Table 1 & Table 2)
(A)Use a multiple-output NAND-gate circuit with minimum gates to realize
W,X,Y,Z(for A,B,C,D and their inverted signal can be used).(10%)
(Hint:the circuit will have 12 gates & 31 gate inputs.)
(B)Realize W,X,Y and Z using a PLA(Programmable Logic Array). Please help
to fill the PLA table2. It is not needed to draw the PLA internal
connection.(10%)
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