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Unformatted text preview: .WWV‘HWh ~ . =5§f/;?;;9. M5”; Iii; ﬂy»)azzwxzwaxwzaﬂﬂy IazywzﬁwwWW/Wzy/Ww‘! Razz/r, ' wanna—Mame“! 144 Unit 5 Write down two different minimum sum—of—products expressions for f. f = .
f= / ‘ V
abc b’c’de + a’c’de
or + b’c’de + a'bc’d
bce’ ab’de + a’c’de // OOOOOOOOOOOOOOOOOO
r each function using aKarnaugh map. Problems
0
(b) f2(d, e, f) = 2 m<0,1,2,4> Find the minimum sum of products f
(d) f4(x: y, Z) = M0 ' M5 Answer: f= a’d'e’ + ace + a’ce’ + bde’ + 5.3
(3) 101(0) by C) = mo + me + ms + m6 (c) f3(r, s, t) = rt' + r's’ + r’s (a) Plot the following function on a Karnaugh map. (Do n plotting.) 5.4 F(A,B,C,D) = BD' + B’CD + ABC + ABC'D + B’D'
\ (b) Find the minimum sum of products.
(0) Find the minimum product of sums. A switching circuit has two control inputs (C1 and C2), two data inputs output (Z). The circuit performs one of the logic operations
uts. The function performed depends on or XOR (exclusive OR) on the two data inp
control inputs: 5.5 Function Performed
by Circuit
OR
XOR I
AND
EQU (a) Derive a truth table for Z. (b) Use a Kamaugh map to ﬁnd a minimum ANDOR gate circuit to realize Z. Find the minimum sumof—products expression for each
prime implicants in your answer and tell which minterm
(a) f(a, b, c, d) = 2 m (0, 1, 3, 5, 6, 7,11, 12,14) (b) f(a, b, c, d) = HM (l, 9,11,12, 14)
(c) f(a, b, c, d) = HM(5, 7,13,14, 15)  HD (1,2, 3, 9) 5.6
makes each one essential. (X 1 and X2), and one, AND, OR, EQU (equivalence),
the function. Underline the essen E
i
i
‘1
z
.7
S
i
<9
i ot expand to minterm form before tial Karnaugh Maps 145 5.7 Find the minimum sumof—products expression for each function.
(a) ﬂu, b, c, d) = E m (0, 2, 3, 4, 7, 8, 14)
5. (b) f(a, b, c, d) = 2m(l,2,4, 15) + 2d(0,3, 14)
____’__ " (c) f(a, b, c, d) = HM(1, 2, 3, 4, 9, 15)
s, (d) f(a, b, c, d) = HM(0, 2, 4, 6, 8)  HD(1,12,9,15) 5.8 Find the minimum sum of products and the minimum product of sums for each function:
(a) ﬂat, [7, c, d) = HM(O, 1, 6, 8, 11, 12)  HD (3, 7, 14, 15)
(b) f(a, b, c, d) = 2 m (1, 3, 4, 11) + 2 d(2, 7, 8,12,14,15) 5.9 Find the minimum sum of products and the minimum product of sums for each function:
(a) F(A, B, C, D, E) = E m(0, 1, 2, 6, 7, 9, 10, 15, 16, 18, 20, 21, 27,30)
+ 2 d(3,4,11, 12,19)
(b) F(A,,B, C, D, E) = HM(0, 3, 6, 9, 11, 19, 20, 24, 25, 26, 27, 28, 29, 30)
 HD(1,2,12,13) 5.10 F (a, b, c, d, e) = 2 m (0, 3, 4, 5,6,7, 8, 12, 13, 14, 16, 21, 23, 24, 29, 31)
(a) Find the essential prime implicants using a Karnaugh map, and indicate why each one of the chosen prime implicants is essential (there are four essential prime implicants):
Eomibefore : (b) Find all of the prime implicants by using the Karnaugh map. (There are nine in all.) 5.11 Find a minimum productof—sums solution for f. Underline the essential prime implicants. f(a, b, c, d, e) = 2 m (2, 4, 5, 6', 7, 8,10,12,14,16,19, 27, 28, 29, 31) + 2 d(l, 30) 5.12 Given F = AB’D’ + A'B + A’C+ CD. (a) Use a Karnaugh map to ﬁnd the maxterm expression for F (express your answer in both
decimal and alphabetic notation). (b) Use a Karnaugh map to ﬁnd the minimum sum—ofproducts form for F’.
(c) Find the minimum product of sums for F. X2), and one
aqUiValence),
yends on the 5.13 Find the minimum sum of products for the given expression. Then, make minterm5 a don’t
care term and verify that the minimum sum of products is unchanged. Now, start again with the original expression and ﬁnd each minterm which could individually be made a don’t
care without changing the minimum sum of products. F(A, B, C, D) = A’C'+ B’C+ ACD’+ BC’D 5.14 Find the minimum sum of products for each of these functions. .
. (a) f1(A, B, C) = m1+ m3 + m + m6 (b) f2(d, e,f) = 2 m(1, 4, 5, 7) (C) f3(1: s, t) = r’t’ + rs' + rs (d) f1(a, b, c) = m3 + m4 + m6 + m7 (e) f2(m P; 4) = 2 m (2, 3, 5, 7)‘ (f) 1209 )4 Z) = M3 Ms :Z. .e the essﬁ‘enﬁal' sent12,1. 5.1 5 Find all possible minimum sumof—products expressions for each function. I (a) f(a, b, c) = HM(2, 3, 4) (b) g(d, e,f) = 2 m(l, 6) + 2 d(O, 3, 5)
(0) f0), (1: r) = (p + q’ + r)(P' + q + r') A (d) f(& t, u) = 2m(1,2,.3) + 2 d(O, 5, 7) (e) ﬂa’b’ c) =HM(3’4) (f) g(d, e,f)=2m(1,4, 6)+2d(0, 2, 7) & ' " .{////}"/}7.&7////7 y/////l//////////l//// 146 Unit 5 5.16 '(a) Plot (b) Find the minimum
(0) Find the minimum 5.17 Work Problem 5.16 for th 5 . 1 8 A switching circuit h
output (Z). The circu plotting.) F (A,B,C,D) = A’B’ sum of products.
product of sums. f (A,B, C,D) table: 5.19 5.20 5.21 5.22 (a) Derive a truth table for Z.
(b) Use a Karnaugh map to Find the minimum sum
(a) 2 m (0, 2, 3, 5, 6, 7, 1 the following function on a Kamaugh e following:
= A’B’ + A’B'C’ + A’BD’ as two control inputs (C1 and C2), two data inp it performs logic operations on map. (Do not expand to minterm fo rm before + CD’ + ABC + A'B'C'bﬁ 4 ABCD’ ' + AC'D.+ A'BD+ AB'CD'I
uts (X1 and X2), and one the two data inputs, as shown in this Function Performed 1, 12, 13) (b) 2m(2,4,8)+2d(0,3,7) (c) 2 m (l, 5, 6, 7,13) + (d) f(w, x, y, z)
(e) [I M (0, l, 2, 5, 7, 9, Work Problem 5.1
(a) f(a, b, c, d) =
(b) f(a, b, c, d) =
(c) f(a, b, c, d) =
(d) f(a, b, c, d) = Find the minimum produ cants in your answe .
(a) HM (0, 2, 4, 5,
(b) 2 m (1, 3, 8, 9,15) Find a minimum sum— function:
(a) f(A, B, C, D) = II
(b) f(w, x, y, z) = =2m(0,3,5,7,8, 2 d (4, 8) 11) . 9 for the following:
2 m (1, 3, 4, 5, 7, 9,13,15)
EM (0, 3,5, 8,11) 2 m (0, 2, 6, 9,13,1
II M (O, 2, 6, 7, 9, 12, 13) + 2d(6,7, l2) of—products and a minimum pr M (O, 2, 10, 1 2 m(0, 3, 5,7, 8, 1, 12,
9, 10 ﬁnd a minimum OR—AND ct of sums for the following. Underline 6, 9, l4)  H D(10,11) ! gate circuit to realize Z. of—products expression for 9, 10, 12,13)+ 2 d (l, 6, ll, 14)
II D (4, 10, 13) 4) + 2d(3, 8,10) . HD(1,3,5) the essential prime impli— oduct—of—sums expression for 680 14,15)  H D (5, 7)
12, 13) + 2 d(l, 6,11, 14) Karnaugh Maps 147 before 5.23 A logic circuit realizes the function F(a, b, c, d) = a’b’ + a’cd + ac’d + ab’d’. Assuming that a = c never occurs when b = d = 1, ﬁnd a simpliﬁed expression for F.
5.24 Given F = AB'D’ + A’B + A’C + CD. , x
' (3) Use a Karnaugh map to ﬁnd the maxterm expression for" F (express your answer in both
decimal and alphabetic notation). , .
(b) Use a Karnaugh map to ﬁnd the minimum sum of products form for F
(c) Find the minimum product of sums for F. ‘ I 5.25 Assuming that the inputs ABCD = 0101, ABCD = 1001, ABCD = 1011 never Occur, ﬁnd
a simpliﬁed expression for F = A’BC’D + A’B’D + A’CD + ABD ABC , and one
vn in this 5.26 Find all of the prime implicants for each of the functions plotted on page 142. 5.27 Find all of the prime implicants for each of the plotted functions: 5.28 F(a, b, c, d, e) = 2 m(0, 1,4,5, 9,10, 11, 12,14,18, 20, 21,22, 25, 26, 28)
(a) Find the essential prime implicants using a Karnaugh map, and indicate why each one
of the chosen prime implicants is essential (there are four essential prime implicants).
(b) Find all of the prime implicants by using the Karnaugh rnap (there are 13 in all). 5.29 Find the minimum sumofproducts expression for F. Underline the essential prime impli
cants in this expression.
(a) f(a, b, c, d, e) = 2 m(0, 1, 3,4, 6, 7, 8, 10, 11, 15, 16, 18, 19, 24, 25, 28, 29, 31)
+ 2 d (5, 9, 30)
(b) f(a, b, c, d, e) = 2 m (1, 3, 5, 8, 9, 15, 16, 20, 21, 23, 27, 28, 31) 5.30 Work Problem 5.29 with
F(A, B, C, D, E) = [I M(2, 3, 4, 8, 9, 10, 14, 15, 16, 18, 19, 20, 23, 24, 30,31) ...
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This note was uploaded on 01/15/2012 for the course EEL 3701c taught by Professor Gugel during the Spring '05 term at University of Florida.
 Spring '05
 Gugel

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