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Department of Electrical and Computer Engineering
University of Minnesota
EE2301
Fall 2009
Introduction to Logic Design
L. L. Kinney
Discussion V Solutions
Oct. 89:
Topics are minimization and an example design.
1.
The 4variable function f(A,B,C,D) is f =
∑
m(0, 1, 3, 5, 6, 7, 10, 11, 12, 13).
(a) Use the simplification identity to find all prime implicants of f.
(b) Repeat (a) using the binary notation for the products (QuineMcCluskey procedure).
(c) Repeat (a) using the decimal notation for the products.
(d) Use a Karnaugh map to find all prime implicants of f and to identify the minimum
SOP expression for f.
(e) Use a Karnaugh map to find all prime implicates of f and then find the minimum
productofsums expression for f.
(A prime implicate is the dual of a prime implicant,
i.e., it is a minimum sum
contained in f.
The complement of a prime implicate of f is
a prime implicant of f
′
.)
(f) What is the minimum number of NAND gates and inverters required to realize this
function in a twolevel circuit?
(g) What is the minimum number of NOR gates and inverters required to realize this
function in a twolevel circuit?
(h) If 7400 series logic is used, which solution, (e) or (f), requires the fewest chips
(packages)?
How many chips and which ones?
1.
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 Fall '09
 LarryKinney
 prime implicants, priority encoder, higher priority encoder

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