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STUDENT ID NUMBER___________________
University of Waterloo
Midterm Examination
SPRING TERM 2007
Course Number
SYDE 192
Course Title
Digital Systems
Instructor
C. Gebotys
Date of Exam
June 15, 2007
Time Period
12:30-1:20
Duration of Exam
50 minutes
Number of Exam Pages(including this
cover sheet)
6
Exam Type
Closed book
Additional Materials Allowed
NONE
Student Name
Student ID Number
ANSWERS…
_____________________________________________
Notes: Show all your work. If necessary, Clearly state any assumptions made.
Question
1. (4 marks)
2. (9 marks)
3. (5 marks)
4. (6marks)
5. (6 marks)
TOTAL (30 marks)
Score
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STUDENT ID NUMBER___________________
1. [4 marks]Answer the Questions below and place your final answer in the BOX
provided
a) [1 marks] The binary-coded decimal code ( 01010011 )BCD represents
in hexadecimal:
(
35
)16
b) [1 marks] The 8’s Complement of (4320)8 is equal to C, where
C = 3460
c) [1 marks] Solve using 2’s complement arithmetic
(11101)2 + (10011)2
=(
10000
)2
[1 mark] In the above computation of 1c), has overflow occurred?
___________No__________(Yes or No)
2.
[9 marks] Given the first column below describing the minterms of f(a,b,c,d),
complete the remaining columns where appropriate using the tabulation method or
Quine-McCluskey method. Check off entries where applicable and label minterms.
Quine-McCluskey or Tabulation Method’s Columns:
Column 2
000-,0-00,00-0
00-1,-100,01-0,0-10,001011-,-011
-111,1-11
Column 3
0 0 - -, 0 - - 0
0 – 1 –
- - 1 1
3. [5 marks] Using ONLY Algebraic Simplification, transform the expression, F,
into an equivalent minimum sum of products.
F = (a+cd)(ad + bec)(e + bde)= (a+cd)(ad + bec)(e(1 + bd))
=e(a+cd)(ad + bec)=e(ad+abec+acd+becd)
=e(ad(1+c) + abec+becd)=e(ad+abec+becd)=ade+abec+becd
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STUDENT ID NUMBER___________________
4. [6 marks] Given the Karnaugh map below which defines a signal f(a,b,c,d), find
the ‘best’ all NOR-gate implementation for f(a,b,c,d). The ‘best’ means a
minimum number of gates and for that minimum number of gates, a minimum
number of inputs to gates. Assume inputs are available in true or complement
form. Show your solution using a NOR-gate expression for f . Underline the
essential (e.g. essential prime implicants) components in this expression.
Get the 0’s
F= [(a’ + d)’ + {
(a’+b’ + c) or (b’+c+d’) }’
+(a+b)’ ]’
5.
[6 marks] Write any expression for z in the following circuit. The expression
must contain only ‘and’ , ‘or’ and ‘not’ operators (where + is ‘or’, etc ). Do not
use any exclusive-or operation in the expression.
F=(q1’(xy)’ + q1xy)(x(w+q1)+q2)