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Unformatted text preview: Practice Problem Set #1 Solutions 1. (a) Plot the following function on a Karnaugh Map. (Do not expand before plotting). F(A,B,C,D) = A'B' + CD' + ABC + A’B’CD' + ABCD'
(b) Find the minimum Sum of Products (SOP) expression. (c) Find the minimum Product of Sums (POS) expression. FAB 00 01 11 10
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l Spring 2012 2. Find the minimum Sum of Products (SOP) and minimum Product of Sums (POS) expressions
for each of the following: (a) F(A,B,C,D) = 2111(0. 2, 3, 4. 7, 8, 14) p (A,r5,c,o) : A'c’o’Jr B’c’o’
+ A’cp + NIB/C + ABLOC
F (A,6,C,D) = (6+p')(A’+D').
(A’+5'+¢)(A’kg+c’).
(RVEI*CI+D)‘
(b) F(A,B,C,D) = HM(1, 2, 3, 4, 9, 15)
F AB
CD _ F(A,6,c,v7 = (A‘VE—i’c’).
EﬂEE (“UV'VAw/“Wi (Nash c’m' )‘ mmﬁ [EILEEN A
' Remap) = Ao’+ B’c’p’ + Ec’D + NBC + AB’c: 2 of 10 Spring 2012 3. Find the minimum Sum of Products (SOP) and minimum Product of Sums (POS) expressions
for each of the following: (a) F(A,B,C,D) = Zm(0, 2, 6, 9, 13, 14) + 2d(3, 8, 10) FCA.6,C,D) = CD’+ 13’17’.L
AC’D . F(A,6,C,D) = (Unix Aw’), (6mm), (b) F(A,B,C,D) = HM(0, 2, 6, 7, 9, 12, 13) . HD(1, 3, 5) °° [mam
m [QMIQJQ
mmm
mmmm F(A,B,C,D) a (Amﬂud).
(PH'C'XA'Jr EWC)‘ 11 Pékﬁycm) = AC 4' N6C’+
Ms’b’. 10 3 of 10 Spring 2012 4. Roth & Kinney — problem 5.19. (c) 8.;n3C‘M—IUﬁO z 4of10 hmex. F. !:+X., Spring 2012 (‘I,*xl’+xﬂ(¢t *c;*xa’*x: )(ayq’ 4‘48"“) 290:
“Etta—~— a 0
~. vv‘nwv N; 32.: \
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O 5 of 10 Spring 2012 5. Roth & Kinney — problem 2.13, part (d).
° Determine the Boolean expression that represents the given logic circuit.
0 Use Boolean algebra to simplify the Boolean expression
° Draw the corresponding simpliﬁed logic circuit. I
2‘ “WM + (we I 7 Y x mm H9 (v.55): WIN] 1 KW “a” (Lm)c)/+ D
—’ ((ﬁm)’+c’)+ I)
= Myra/+17 6 of 10 Spring 2012 6. Roth & Kinney — problem 3.13, parts (b) and (c).
(b) [4L’M’+ NM' 4' LM'N”
ILL’M’ Ir N’ (M + LM') [LL’M’Jr “((M4’L) : [LL’M’ + 1,51% MW (57 (l4*L,)<lL’+L/+H)(LI+M+N’)
(L’+ (\L)(w+p))(u+mw’)
(L’ + lad Jr [4H)(L'+M +M’)
(U4, 1LU)(L’+M+M’)
(LW (WXMW'H L’+ [emu + ILIJN’ L’+ MM“. 7 of 10 Spring 2012 7. Roth & Kinney — problem 3.25, pan (d). (A) A’D(l3'+c) + A’D’(E+c/) 4’ ((5% 0X my)
Nb’o + New 4' NBDW A’L'D’ + B'B + 156+
(,6 + cc,’ A'E’D + Na!) + Ix’sv’ + A’c’o’ + [5’(,’ + BC. 8 of 10 Spring 2012 8. Roth & Kinney — problem 4.7. WNW ‘ (Mmum’rc'xm m’ )(k'*b’Lc)‘
' (A’q'a'c’ ) 9 of 10 Spring 2012 9. Determine the minterm and maxterm expansions for the logic functions given below.
' Specify the minterm expansion using “littlem” notation.
° Specify the maxterm expansion using “bigM” notation. (a) F(A,B,C,D)=AB +A'CD
p(k.a,c,o) 2 pa; (co +c'o 4* co'w’b’) 4' Na) (5 445’) M500 + RBC’D + RBCD'+ k6c’o'+ A'BCD + k’lZ/LD
\S B W n, 7 3 u FLk,l5,c,o) z §m(3,7,n,t3,w,tg)
F 058,90) 2 ‘KM(°.I,7',*f,S,(.,8,‘i,to,u) (b) F(A,B,C,D) = (A + B + D').(A' + C).(C + D)
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new»)? ‘ (M 6* c’ ’r 0’ Wk 5 +6: +o’) I I \‘5 I In, I 0" I l 8 ‘ (Ix H3 rap )(N+ B + CroXMBmw )(K 4' 3+ up
4 o (NJ/6’ {:1CVD)(AI‘V3 1c tux AHS'k c+p)( MB +4417). 90mm) 5 Wm(o'~t,%,‘l,lm,l3,l,s)
: “Mkoﬂﬁﬁy‘f‘ﬂhm FLA,6,c,o) 2 §M(z,§,c,7, lo’ll.l'{"l§) 10 0f 10 Spring 2012 ...
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