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Unformatted text preview: CARLETON UNIVERSITY 5( FINAL Name
EXAMINATION April 1996 Number DURATION: 3 HOURS N0 of Students: 94 Department Name & Course Number: Electronice 97.267
Course Instructor(s) T.G. Ray AUTHOIIZKD “CUBQ'CDI
Any books or notes; any non—communicating calculator. Students MUST count the number of pages in this examination question paper before beginning to
write, and report any discrepancy immediately to a proctor. This question paper has eight pages. This examination question paper may not be taken from the examination room,
———m—_—.._____—___—_—___ INSTRUCTIONS: Open book. No talking. Attempt all questions. Place all responses on the front sides of the
examination sheets unless otherwise instructed. If you absolutely must respond to a question
using the answerbook, please put a clear note on the question referring the marker (me!) to your answer. If you do not understand a question or think there is an error, make a reasonable
assumption and state it clearly. Consider only one input to a circuit to change at one time (unless speciﬁcally instructed
otherwise). The exam marks total 95. 1. Short Questions (25 marks total) lai) Redraw the following circuit using only NAND gates and as few inverters as
possible. (3 marks) A 3 F’
A
5 Answer: laii) What two words best describe the two ways in which the NAND implementation
is better than the original? (2 marks) Answer 1 : Answer 2: 11)) Circle all of the prime implicants on the following S—variable Kamaughmap.
Unfilled locations are actually all 0. (4 marks) If you mess up the first map, use this copy: Do 01 1 1 1 o
00
01
11
10
1c) ' delay in the proper place is a practical and sure method of ﬁxing a design i) a static hazard
ii) a dynamic hazard
iii) an essential hazard Answer: yes/no
Answer: yes/no
Answer: yes/no Ii 3 K
1d) Why were the ﬂip—ﬂops used in this course exclusively Dtype, and the use of other
types forever discouraged? (In 25 words or less.) (3 marks) Answer: 1e) What one word best describes the reason why the clock inputs to ﬂip—ﬂops in this
course were always tied together and to one master clock? (One word.) (2 marks) Answer:
It) Give a new equation for
F: ACE+BCD+EB which has no static hazard problems. (4 marks) Answer: F =
1g) Prove or disprove, without the use of Boolean algebra or any theorems, that (A+1§)(K+C)(B+C) = (A+B)(K+C) (4 marks) Answer: 2. Machine (8 marks total) Clk
I
State Rll   Ill  I l I
Output
3.) Fill in the states and the output waveform for the above timing diagram using the state graph given. (6 marks) b) Find an impossibility in the above state graph, circle it, and say what it is. (In 10
words or less.) (2 marks) Answer: 1L Q .i . l.
1 I 1 i ! ::
i i E;
I i i:
E i ‘ l .
l : 1'
i 5'
‘ = i : I:
t : 5.
I !I
i ! i;
i i:
r I i:
l E t i x I i;
\ E ;  E!
l u :'
‘  ..
l i 'i
‘> 3. Synchronous Circuit Design (15 marks total) A Moore machine is to have two inputs, X and Y, and one output, F. X and Y
each receive independent sequences of ls and Os synchronized to a single clock. Design
an efﬁcient circuit, using one ﬂip—ﬂop and a minimum of logic, to make F = 1 whenever
the number of Is received so far in the X sequence PLUS the number of Os received so far
in the Y sequence, is evenly divisable by 2, i.e. divisable by 0, 2, 4 , 6... . Put your solution in the answer—book. Show all of your work. 4. Asynchronous Circuit Design (20 marks total) a) Three individuals, William, Xavier and Yolanda, each have a pushbutton and a
light hooked up to an asynchronous circuit you are to design. The circuit is to indicate who pushes their button ﬁrst, by pennanently lighting their light and forever preventing
the other lights from coming on. The three individual’s push—button inputs are conveniently designated W, X and Y, and the corresponding outputs are Wo, X0 and Y0
(o = output). Considering in more detail the exact operation of the W0 output as an example: We should be set to 1 if and only if:
 the W button is pushed, i.e. W=l,
 while neither the X nor Y buttons are pushed, i.e. XY=00,
— and neither the X nor Y buttons have ever before been pushed, i.e. XoYo=OO. And once We is set to 1 it should stay set forever. The other buttons should make the corresponding circuit outputs behave similarly.
To start the entire circuit in the reset condition there should be an overall RESET input,
which you are assured will be pushed only once to initialize the circuit when it is first
turned on. Your design does not have to consider races or hazards. You may design just
1/3 of the entire circuit, as long as it is representative of the other 2/3. (17 marks) Put your solution in your answerbook. Show all your work. b) For your design, what would be the values of the three outputs if W, X and Y were all depressed at EXACTLY the same time? (Your design doesn’t have to deal with this
situation.) (3 marks) Put your answer for WoXoYo in your answerbook as well. jﬂ 5. Critical Races and Essential Hazards (12 marks total) A speciﬁc asynchronous machine has the transition table shown in the seven
identical copies below. Not everything is represented in the copies, and they may or may not all be needed, while the three at the bottom are spares for rough work or in case you
mess up the earlier ones. a) Circle all the stable states on the first table. Indicate two critical races (if that
many exist), each by arrows showing the paths taken through the nextstate part of the table, from the initial stable state to the ﬁnal stable states. Show only one critical race
per table. Critical Race: AB A+B+
XY=00 01 1 l 10
00 1 l l 1 10 00
01 I 1 01 00 01
1 1 1 1 10 01 11
10 10 10 1 l 01
Critical Race:
AB A+B+
XY=00 01 l l 10
00 ll 1 1 10 00
01 l 1 0 1 00 01
1 1 1 l 10 01 l 1
10 10 10 l 1 01
b) Indicate two essential hazards (if that many exist), each by arrows showing the paths taken through the next—state part of the table, from the initial stable state to the ﬁnal
stable states. Show only one essential hazard per table. Essential Hazard: AB A+B+ XY=OO 01 11 10
00 11 11 10 00
01 11 01 00 01
11 11 10 01 11
10 IO 10 11 01 5. Races and Hazards (cont.) Essential Hazard: AB A+B+ XY=00 01 11 10
00 11 11 10 00
01 11 01 00 01
11 11 10 01 11
10 10 10 11 01 Spare: (For rough work, or write in which part of the question you are using it for or it
won’t be marked.) AB A+B+ XY=00 01 11 10
00 11 11 10 00
01 11 01 00 01
11 11 10 01 11
10 10 10 11 01 Spare: (For rough work, or write in which part of the question you are using it for or it
won’t be marked.) AB A+B+ XY=00 01 11 10
00 ll 11 10 00
01 11 01 00 01
11 11 10 01 11
10 10 10 11 01 Spare: (For rough work, or write in which part of the question you are using it for or it
won’t be marked.) AB A+B+ XY=OO 01 11 10
00 11 11 10 00
01 11 01 00 01
11 11 10 01 11
10 10 10 11 01 6. CriticalRace—Free Asynchronous Circuit State Assignment (15 marks total) For the following state table, revise the table and select a criticalracefree state
assignment Do not change the machine any more than necessary. Keep A as state 001,
and do not increase the number of rows in the table. Enter all of your answers on this page.
Present Next State Output
State XY=OO 01 1 1 10 XY=OO 01 1 1 10
A=001 C D A A —— — 0 0
B B B A B 1 1  1
C C —— E C 0  — 1
D D D — B 1 0 —— ——
E  D E A — —— 1 ——
—— = “don’t care” Answer:
Your state assignment: 0 1 00 01 l 1 10 State table showing just your revisions: (Use letters to represent states, as above.) Present Next State Output State XY=OO 01 1 1 10 XY=00 01 1 l 10
A=OO 1 B C D E / 7/? K ...
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