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Sections E,F Homework Assignment #2
Due: (Sept. 15, 2011) Chapter 2, problems #1, 6, 8, ll, l3, 14, 16, 20, 23 Be sure that you are using the 4th edition. *Demonstrate by means of truth tables the validity of the following identities:
(a) DeMorgan’s theorem for three variables: XTZ = :1; + T7 + 2 (b)*The second distributive 121sz + YZ = (X + Y)(X + Z) (c) XY+}—’Z +X2 = X?+ Y2 +22 Simplify the following Boolean exp
minimum number of literals: (a) ZE+ZBC+§C
(b) (Wym
(c) ABE +AC (d) Z'B‘D +261) +BD (e) (Z + BXZ + E)(A§C) ressions to expressions containing a 2—8. Using DeMorgan’s theorem, express the function F = ABC +ZE+AB (a) with only OR and complement operations.
(13) with only AND and complement operations. W’ 11. For the Boolean functions E and F, as given in the following truth table: y—Ly—IHHOOOOX
HHOOHHOO<
HOD—IOD—‘Ol—‘ON
OHOD—‘Ol—‘l—‘Om
HOOD—*Ol—‘OH'H (a) List the minterms and maxterms of each function. (h) List the minterms oi E and F. (c) List the minterms of E + F and E F. . ((1) Express E and F in sumotminterrns algebraic form.1 .t ls
(e) Simplify E and F to expressions With a minimum of i era . inf I 3. Draw the logic diagram for the following Boolean expressions. The diagram
should correspond exactly to the equation. Assume that the complements of
the inputs are not available. (a) XYZ + X? + X?
(b) BM? +AC) + 504 + BC)
(c) XT’(W + Z) + Wm}? + Z) + WY()_( + Z) . Optimize the following Boolean functions by means of a three—variable map:
(a) F(X,Y,Z) = Em(0,2,6,7) (b) F(X, Y, Z) = 2m(0,1,2,4) (c) F(A,B,C) = Em(0,2,3,4,6) (d) F(A,B, C) = 2m(0,2,3,4,5,7) 2—16. Optimize the following Boolean functions by means of a fourvariable map:
(a) F(A,B,C,D) = 2m(2,3,8,9,10,12,13,14)
' (b) F(W,X, Y,Z) = Em(0,2,5,6,8,10;13,14,15)
(c) F(A,B,C,D) = 2m(0,2,3,7,8,10, 12,13) 2—20. Optimize the following Boolean functions by ﬁnding all prime implicants
and essential prime implicants and applying the selection rule: (a) F(W,X,Y,Z) = 2m(0,2,3,5,7,8,10,11,12, 13)
(b) F(A,B,C,D) = 2m(3,4,5,7,9,13,14,15)
(c) F(W,X,Y,Z) = 2m(0,2,4,6,7,8,9,12,13,15) 2—23. Optimize the following functions into (1) sumof—products and (2) product—
ofsums forms: (a) F(A,B,C,D) = Em(0,1,5,7,8,10, 14,15)
(b) F(W,X,Y,Z) = HM(3,11,13, 15) ...
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