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Your Name: _________________________________
UNIVERSITY OF CALIFORNIA AT BERKELEY
BERKELEY • DAVIS • IRVINE • LOS ANGELES • RIVERSIDE • SAN DIEGO • SAN FRANCISCO SANTA BARBARA • SANTA CRUZ Department of Electrical Engineering and Computer Sciences
CS 150 - Spring 1990 Prof. A. R. Newton
Final Examination
Thursday 5/ (Open Wakerly, Calculators OK, 3 hrs)
Include all final answers in locations indicated by boxes on these pages. Use reverse side of sheets for all working. SHOW ALL WORKING USED TO ARRIVE AT ANSWERS. If necessary, attach additional sheets by staple at the end. BE SURE TO WRITE YOUR NAME ON EVERY SHEET. There are 6 questions and 100 points, as indicated.
(1) (a) Represent the following sentences by a single Boolean equation: "The tape drive motor for a computer tape drive should be running iff: (i) the tape is properly threaded, (ii) an end-of-tape signal is not present, and (iii) the tape drive is in the manual mode and the motor start button has been pressed, or it is in the automatic mode and the "tape on" signal signal from the computer is present."
1(a) (6pts) Definition of terms:
Boolean Equation:
(b) Given that F = A
_
B
_
+ A
_
C
_
+ C
_
D
_
+ B
_
C D
(i) Use a Karnaugh map to find the maxterm representation of F. Express your answer in standard decimal notation.
(ii) Use the K-map to find the minimum sum-of-products form for F
_
. Express in algebraic form. (iii) Find the minimum product-of-sums for F. Express in algebraic form.
1(b) (9pts) (i) Maxterm representation: F =
(ii) Minimum S-of-P form: F
_
(iii) Minimum P-of-S form: F =
(additional space for working, Problem 1)
2(b) (9pts)
4-to-
MUX
F
(additional space for working, Problem 2)
Your Name: _________________________________
(3) This problem concerns the design of a parallel adder for adding three positive binary numbers. These numbers are designated Xn...X 3 X 2 X 1 , Yn...Y 3 Y 2 Y 1 and Zn...Z 3 Z 2 Z 1. A typical cell used in the adder is shown below. Note that there are two carry signals, C and D, propagating between cells. Two carry signals are required because when three binary digits are added to the carry coming into the cell, the carry to the next cell may be either 0, 1, or 2 (coded as Ci+1Di+1= 00, 01, and 10 respectively). (a) Derive a truth table which specifies the complete operation of a typical cell (your table should contain some "don't cares"). (b) Derive a Boolean equation for Si in minimum form (Equations for Ci+1 and Di+1 are not required.).
Typical Cell
Xi Yi^ Zi
Ci
D i
Ci+
D i+
Si
3(a) (6pts) Truth Table:
3(b) (6pts) Si =
Your Name: _________________________________
(4) For the following state table, where X 1 and X 2 are inputs and Z 1 and Z 2 are outputs:
(a) Use the three guidelines for state assignment to determine which of the three possible non- equivalent state assignments should give the best solution. Show all steps and explain your choice. Do not attempt to reduce the state table.
(b) Using your answer to (a) above, derive T flip-flop input equations and the output equations. All equations stated should contain the minimum number of literals. Show all steps.
X1X2 = X1X2=
A A C B D 00 00 00 00
B B B D D 00 00 10 10
C C A C A 01 01 01 01
D B B C A 01 01 10 10
next state output Z 1 Z 2
4(a) (8pts) State codes:
A = B = C = D =
4(b) (10pts) Equations:
T1 =
T2 =
Z1 =
Z2 =
(additional space for working, Problem 4)
5(c) (6pts) Merger Diagram:
5(d) (7pts) Minimum-Row Merged Flow Table:
(additional space for working, Problem 5)
Your Name: _________________________________
(additional space for working, Problem 5)
Your Name: _________________________________
(additional space for working)
(additional space for working)
