Download Midterm Exam 1 with Questions - Digital Logic Design | 332 231 and more Exams Electrical and Electronics Engineering in PDF only on Docsity!
Department of Electrical and Computer Engineering
Fall 2004
14:332:231 DIGITAL LOGIC DESIGN
Last Yearโs Midterm I
Question 1 (18 points) You are given two signed integers in different number systems.
1A. (2 points) What are the values of the two numbers in the decimal system?
1B. (2 points) What is the value of , the shortest word-length of a computer using
twoโs-complement representation, which can represent all of these numbers. What is the largest and the smallest number which can be represented?
1C. (4 points) Give the -bit twoโs-complement representations of the two numbers,
where is the value determined in Question 1B.
1D. (4 points) Compute
using twoโs-complement arithmetic. Convert the result into the decimal system and check that it is true. For full credit you must show all the computational steps. 1E. (6 points) Repeat Question 1D for
. Explain the result. !!!The next page is also for Question 1!!!
Question 2 (24 points)
You are given the following circuit
F(A, B, C, D)
A
C
B
D
2A. (8 points) What is the expression of the logic function
2B. (10 points) Using the Boolean algebra obtain the simplest possible expression for
. You are not allowed to use Karnaugh maps in this problem.
2C. (6 points) Mark on the circuit diagram the values of the gate outputs for the input combination
, where
can be either 0 or 1. Does the result agree with Question 2B? !!!The next page is also for Question 2!!!
3C. (12 points) The propagation delays for the gates needed for Question 3B are Gate
(ns)
(ns) NOT 1 1 2-input AND 3 2 3-input AND 5 2 2-input OR 1 1
Assume that the inputs A,B,C all have value zero and the input D is according the waveform below. Draw the intermediate waveforms D L, O2AND (output of the 2-input AND), O3AND (output of the 3-input AND) and that of the output F at the correct timescale.
t (nS)
2 4 6 8 10 12 14 16 18
F
D
D_L
O2AND
O3AND
3D. (8 points) How should the values of
and
for the 2-input AND gate be changed to remove the glitch occuring at the output. !!!The next page is also for Question 3!!!
Question 4 (26 points)
4A. (4 points) Derive the truth table of the logic function
4B. (4 points) Provide the functional decomposition of F(W,X,Y,Z). 4C. (10 points) Using Question 4B implement
with the 74x153 provided and a single OR gate. You can assume that both the direct and complement values of a variable, e.g.,
are available. Draw your circuit here.
!!!QUESTION 4 CONTINUES ON THE NEXT PAGE!!!
B. (7 points) Using the information about the โdonโt-careโ inputs obtain the minimal SOP expressions of these two logic functions.
C. (6 points) Draw the logic diagram of the circuit controlling the segments and , using only NAND gates. You can assume that both the direct and complemented values are available for the input variables.
D. (10 points) In practice we want to make sure that the display can also be blanked. This is usually achived by a signal which forces the input to become
Will this method work in our โdonโt-careโ approach? Which of the two segments or (if any) will not be blanked? Explain your answer in detail.
Question X (12 points) The truth table for a custom 4x3 priority encoder is given below. Here D0, D1, D2, D3 are inputs and Y0, Y1, Y2 are the output lines.
D0 D1 D2 D3 Y0 Y1 Y x x x 1 1 1 0 x x 1 0 0 0 0 x 1 0 0 1 0 1 1 0 0 0 1 1 1
A. (2 points) Which line has the highest priority?
B. (6 points) Use Karnough maps to derive the minimal sum of product expressions for Y0, Y1 and Y2. Those input combinations that are not specified in the above truth table should be treated as donโt cares.
C. (4 points) Implement the AND-OR circuit for the expressions obtained in part B.
Question X (18 points) You are given four signed integers in different number systems.
A. (2 points) What is the value of the shortest word-length of a computer using twoโs- compliment representation, which can represent all of these numbers. What is the largest and the smallest number which can be represented?
B. (8 points) Give the -bit twos-compliment representations of the four numbers where
is the value determined in
C. (4 points) Prove using twoโs-compliment arithematic that
. For full credits, show the steps.
D. (4 points) Compute using twoโs-compliment arithematic
. Is the result correct? Explain your answer.
Question X (28 points) At the input of a logic circuit the signals A, B, C are measured and at the output the signal OUT. The observed waveforms are as shown below where the output takes into account the propogation delays in the circuit.
Voltage (V)
A
B
C
OUT
Time (nS)
A. (10 points) Write the truth table of the output as a function of the input.
B. (4 points) Describe the truth table as a minterm list.
C. (5 points) What is the minimal sum of products expression of the logic function?
D. (5 points) Draw the AND-OR circuit implementing the above function and show all the intermediate values on the diagram for ABC=011.
E. (4 points) Which of the following condition(s) yield OUT=1? (a) All three input bits are 0. (b) One input bit is 1.
