Eecs:1100 Digital Logic Design Final Examination Eith Answers - Dr. Anthony D. Johnson, The University Of Toledo Page 2
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8The University of Toledo
f15fs_dild7.fm - 2
EECS:1100 Digital Logic Design
Dr. Anthony D. Johnson
Student
name
______________________________________
Problem 1
12 points
Given is a logic (switching) function F
in the decimal list sum-of-minterms representation (1-1).
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(A,B,C,D) = Σ( 3, 4, 6, 8, 9, 12, 14)
F
(1-1)
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d(A,B,C,D) = Σ(0, 2, 7, 13)
Problem statement
On the example of given logic function F
demonstrate an ability to:
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1. derive a Karnaugh map representation of the function F
,
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2. use the Karnaugh map method to derive a minimal number of literals expression of F
and F
,
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3. design the two-level NAND-NAND implementation of the SOP form of function F
, and the
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two-level NOR-NOR implementation of the POS form of function F
, as specified under 1.4
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and 1.5 below.
Hint #1
For full credit: all equations, all answers to questions, all circuit models and other
graphical representations are expected to be entered into the space designated for them;
all shown numerical results must be preceded by the symbolic and numeric expressions
whose evaluation produces these numerical results.
Solution
An explicit demonstration of understanding the following solution steps is expected.
1.1 Prepare the Karnaugh map representation of the function F
, and place a copy of it into each of the
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2
spaces reserved for Figures 1-1(a) and 1-1(c).
CD
CD
00
01
11
10
00
01
11
10
AB
AB
d
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d
d
1
d
00
00
1
d
1
1
d
1
01
01
1
1
d
d
11
1
11
1
1
1
10
10
1
1
(a)
(c)
(b)
(b)
F
=
(B + D)⋅(A + C)⋅(A + C)
F
=
B⋅D + A⋅C + A⋅C
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(d)
(b)
Figure 1-1 Representation forms of the function F
. (a)Karnaugh map. (c)Karnaugh map. (b)Minimum number
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of literals SOP representation of F
. (d))Minimum number of literals POS representation of F
.
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