Title | Solution Manual of Digital Logic And Computer Design 2nd Edition Morris Mano |
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Bismillah hir Rehman nir Raheem ------------------------------------Assalat o Wasalam o Allika Ya RasoolALLAH Solution Manual of Digital Logic & Computer Design (2 Ed.) th Morris Mano Ch Ch Published By: Muhammad Hassan Riaz Yousufi To Read Online & Download: WWW.ISSUU.COM/SHEIKHUHASS...
Bismillah hir Rehman nir Raheem ------------------------------------Assalat o Wasalam o Allika Ya RasoolALLAH
Solution Manual of Digital Logic & Computer Design (2 Ed.) th
Morris Mano
Ch
Ch
Published By: Muhammad Hassan Riaz Yousufi
To Read Online & Download:
WWW.ISSUU.COM/SHEIKHUHASSAN
Problem Solutions to Problems Marked With a * in Logic Computer Design Fundamentals, Ed. 2
CHAPTER 1 © 2000 by Prentice-Hall, Inc.
1-1. Decimal, Binary, Octal and Hexadecimal Numbers from (16)10 to (31)10 Dec Bin Oct Hex
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 0000 1 0001 1 0010 1 0011 1 0100 1 0101 1 0110 1 0111 1 1000 1 1001 1 1010 1 1011 1 1100 1 1101 1 1110 1 1111 20 21 22 23 24 25 26 27 30 31 32 33 34 35 36 37 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
1-4. ( 1101001 ) 2 = 2 6 + 2 5 + 2 3 + 2 0 = 105 ( 10001011.011 )2 = 2 7 + 2 3 + 2 1 + 2 0 + 2 –2 + 2 – 3 = 139.375 ( 10011010 ) 2 = 2 7 + 2 4 + 2 3 + 2 1 = 154
1-7. Decimal
Binary
Octal
369.3125
101110001.0101
561.24
Hexadecimal 171.5
189.625
10111101.101
275.5
BD.A
214.625
11010110.101
326.5
D6.A
62407.625
1111001111000111.101
171707.5
F3C7.A
1-9. 7562/8
=
945 + 2/8
➔
2
945/8
=
118 +1/8
➔
1
118/8
=
14 + 6/8
➔
6
14/8
=
1 + 6/8
➔
6
1/8
=
1/8
➔
1
0.45 × 8
=
3.6
➔
3
0.60 × 8
=
4.8
➔
4
0.80 × 8
=
6.4
➔
6
0.20x8
=
3.2
➔
3
(7562.45)10
=
(16612.3463)8
b)
(1938.257)10
=
(792.41CA)16
c)
(175.175)10
=
(10101111.001011)2
a)
1
Problem Solutions – Chapter 1
1-11. a)
(673.6)8
=
(110 111 011.110)2
=
(1BB.C)16
b)
(E7C.B)16
=
(1110 0111 1100.1011)2
=
(7174.54)8
c)
(310.2)4
=
(11 01 00.10)2
=
(64.4)8
1-15. a)
(BEE)r = (2699)10 11 × r 2 + 14 × r 1 + 14 × r 0 = 2699 11 × r 2 + 14 × r – 2685 = 0
By the quadratic equation: r = 15 or r ≈ –16.27 ANSWER: r = 15 b)
(365)r = (194)10 3 × r 2 + 6 × r 1 + 5 × r 0 = 194
3 × r 2 + 6 × r – 189 = 0 By the quadratic equation: r = -9 or 7 ANSWER: r = 7
1-17. (694)10
=
(0110 1001 0100)BCD
(835)10
=
(1000 0011 0101)BCD
1 0110
1001
0100
+1000
+0011
+0101
1111
1100
1001
+0110
+0110
+0000
0001 0101
1 0010
1001
1-20. a) (0100 1000 0110 0111)BCD
=
(4867)10
=
(1001100000011)2
b) (0011 0111 1000.0111 0101)BCD
=
(378.75)10
=
(101111010.11)2
1-23. a)
(101101101)2
b)
(0011 0110 0101)BCD
c)
0011 0011
0011 0110
0011 0101ASCII
1-25. BCD Digits with Odd and Even Parity Odd Even
0 1 0000 0 0000
1 0 0001 1 0001
2 0 0010 1 0010
3 1 0011 0 0011
4 0 0100 1 0100
2
5 1 0101 0 0101
6 1 0110 0 0110
7 0 0111 1 0111
8 0 1000 1 1000
9 1 1001 0 1001
Problem Solutions to Problems Marked With a * in Logic Computer Design Fundamentals, Ed. 2
CHAPTER 2 © 2000 by Prentice-Hall, Inc.
2-1. a)
XYZ = X + Y + Z
Verification of DeMorgan’s Theorem X 0
Y 0
Z 0
XYZ 0
XYZ 1
X+Y+Z 1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
X + YZ = ( X + Y ) ⋅ ( X + Z )
b)
The Second Distributive Law (X+Y)(X+Z)
X 0
Y 0
Z 0
YZ 0
X+YZ 0
X+Y 0
X+Z 0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
c) X 0
0
XY + YZ + XZ = XY + YZ + XZ Y 0
Z 0
XY 0
YZ 0
XZ XY+YZ+XZ XY 0 0 0
YZ 0
XZ XY+YZ+XZ 0 0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
2-2. a)
X Y + XY + XY
=
= (XY+ X Y ) + (X Y + XY) = X(Y + Y) + Y(X + X) + =X+Y
1
X+Y
Problem Solutions – Chapter 2 b)
A B+ B C + AB + B C = 1 = (A B+ AB) + (B C + B C) = B(A + A) + B(C + C) =B+B =1
c)
Y+XZ+XY
=X+Y+Z
=Y+XY+XZ = (Y + X)(Y + Y) + X Z =Y+X+XZ = Y + (X + X)(X + Z) =X+Y+Z d)
X Y + Y Z + XZ + XY + Y Z
= X Y + XZ + Y Z
= X Y + Y Z(X + X) + XZ + XY + Y Z = X Y + X Y Z + X Y Z + XZ + XY + Y Z = X Y (1 + Z) + X Y Z +XZ + XY + Y Z = X Y + XZ(1 + Y) + XY + Y Z = X Y + XZ + XY (Z + Z)+ Y Z = X Y + XZ + XY Z +Y Z (1 + X) = X Y + XZ(1 + Y) + Y Z = X Y + XZ + Y Z
2-7. a)
X Y + XYZ + XY = X + XYZ = (X + XY)(X + Z) = (X + X)(X + Y)(X + Z) = (X + Y)(X + Z) = X + YZ
b)
X + Y(Z + X Z) = X + YZ + X Y Z = X + (YZ + X)(YZ + YZ) = X + Y(X + YZ) = X + XY + YZ = (X + X)(X + Y) + YZ = X + Y + YZ = X + Y
c)
WX(Z + YZ) + X(W + W YZ) = WXZ + WXYZ + WX + WXYZ = WX + WXZ + WXZ = WX + WX = X
d)
( AB + AB ) ( CD + CD ) + AC = ABCD + ABCD + ABCD + ABCD + A + C = A + C + ABCD = A + C + A(BCD) = A + C + BCD = A + C + C(BD) = A + C + BD
2-9. a)
F = (A + B )( A + B )
b)
F = ( ( V + W )X + Y )Z
c)
F = [ W + X + ( Y + Z ) ( Y + Z ) ] [ W + X + YZ + YZ ]
d)
F = ABC + ( A + B )C + A ( B + C )
2
Problem Solutions – Chapter 2
2-10. Truth Tables a, b, c X 0
Y 0
Z 0
A 0
B 0
C 0
b
0
1
W 0
X 0
Y 0
Z 0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
a)
a
Sum of Minterms:
c
XYZ + XYZ + XYZ + XYZ
Product of Maxterms: (X + Y + Z)(X + Y + Z)(X + Y + Z)(X + Y + Z) b)
ABC+ABC+ABC+ABC
Sum of Minterms:
Product of Maxterms: (A + B + C)(A + B + C)(A + B + C)(A + B + C) c)
WXYZ+WXYZ+WXYZ+WXYZ+WXYZ+WXYZ
Sum of Minterms:
+WXYZ Product of Maxterms: (W + X + Y + Z)(W + X + Y + Z)(W + X + Y + Z) (W + X + Y + Z)(W + X + Y + Z)(W + X + Y + Z) (W + X + Y + Z)(W + X + Y + Z)(W + X + Y + Z)
2-12. a)
(AB + C)(B + CD) = AB + BC + ABCD = AB + BC s.o.p. = B(A + C) p.o.s.
b)
X + X ((X + Y)(Y + Z)) = (X + X)(X + (X + Y)(Y + Z))
c)
(A + BC + CD)(B + EF) = (A + B + C)(A + B + D)(A + C + D)(B + E)(B + F) p.o.s.
= (X + X + Y)(X + Y + Z) = X + Y + Z s.o.p. and p.o.s. (A + BC + CD)(B + EF) = A(B + EF) + BC(B + EF) + CD(B + EF) = AB + AEF + BCEF + BCD + CDEF s.o.p.
2-15. a) 1 X
b)
Y 1 1 Z X Z + XY
1
1 A
c)
B 1
1
1 C A + CB
3
1
B 1
1
1
A 1
1
1
C B+C
Problem Solutions – Chapter 2
2-18. a)
b)
1
1
1
1
W
1
1
1
1 1
X
1
A 1
Z Σm ( 3, 4, 5, 7, 9, 13, 14, 15 )
Σm ( 3, 5 , 6 , 7 )
1 1
1
Z
C 1
1
Y 1 X
c)
Y
1
B
1 1
D Σm ( 0, 2 , 6, 7 , 8 , 10, 13, 15 )
2-19. Using K-maps: a) Prime = XZ, WX, X Z, W Z
b) Prime = CD, AC, B D, ABD, B C
Essential = XZ, X Z
c) Prime = AB, AC, AD, BC, BD, CD
Essential = AC, B D, ABD
Essential = AC, BC, BD
2-22. Using K-maps: b) s.o.p.A C + B D + A D
a) s.o.p. CD + AC + B D p.o.s.(C + D)(A + D)(A + B + C)
c) s.o.p.B D + ABD + (ABC or ACD)
p.o.s.(C + D)(A + D)(A + B + C)
p.o.s.(A + B)(B + D)(B + C + D)
2-25. b)
a) B A
1
1
X
X
1
1
W
C Primes = AB, AC, BC, A B C Essential = AB, AC, BC F = AB + AC + BC
c)
Y 1
1 1
X
X
1 1
1
1
X A
X
Z Primes = X Z, XZ, WXY, WXY, W Y Z, WYZ Essential = X Z F = X Z + WXY + WXY
2-28. a) B A C D B A C D B A C D B A C D
4-input NAND from 2-input NANDs and NOTs
A B
A B
C D
C D
A B
A B
C D
C D
4
C X X X 1
1
1
1 X
1
X X
B
D Primes = AB, C, AD, BD Essential = C, AD F = C + AD + (BD or AB)
Problem Solutions – Chapter 2
b)
A B
A B A B
C
C D C D
D
2-30. a)
C 1 1 1 1
A 1
1
1
1
B
b)
A B C A C A D
W
D F = ( A + B + C )( A + C ) ( A + D )
W X W X Y Z Y Z A
Y 1
1
1
1
X
Z F = ( W + X )( W + X )( Y + Z ) ( Y + Z )
2-34. X ⊕ Y = XY + XY Dual (X ⊕ Y ) = Dual ( XY + XY ) = ( X + Y )( X + Y ) XY + XY = ( X + Y ) ( X + Y ) = ( X + Y )( X + Y )
2-37. 16 inputs 16 inputs 6 inputs
2-39. 4 × 0.5 = 2 ns
2-44. P-Logic X
Y NAND
NOR
X
Y NAND
L
L
H
H
0
0
L
H
H
L
0
H
L
H
L
H
H
L
L
N-Logic NOR
X
Y NAND
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
5
NOR 0
Problem Solutions to Problems Marked With a * in Logic Computer Design Fundamentals, Ed. 2
CHAPTER 3 © 2000 by Prentice-Hall, Inc.
3-2. D
T1 = T3 = X = = Y = =
T3 X
C B
Y
T4
T1
A
BC, T2 = AD 1 T4 = D + BC , T3T4 D + BC T2T4 AD(D + BC) = A BCD
T2
Y X
1 1
X 0 0 0 0 1 1 1 1
1 Z
XZ + ZY
X Z
Y 0 0 1 1 0 0 1 1
Z 0 1 0 1 0 1 0 1
T1 1 1 1 1 1 1 0 0
T2 1 1 1 1 0 0 1 1
T4 1 0 1 1 1 1 1 0
T5 1 0 1 1 1 0 1 0
F 0 1 0 0 0 1 0 1
T2
X F
Z Y
T3 1 1 0 0 1 1 1 1
T4
T1
F
Y Z
T5
T3
3-3. X 0 0 1 1
X T2 F
T1
T3
Y
Y 0 1 0 1
T1 1 0 0 0
T2 0 1 0 0
T3 0 0 1 0
F 1 0 0 1
3-6. A
M = AS + BS
S
M
B
T1 = ZY + ZY Y X
Z Y
A S B
M
A S B
M
F
F = YX + T1X
= YX + X(ZY + ZY)
= XY + XYZ + XYZ
T1
X Z
A S B
G = M
G
=
1
T1X + ZX
= XZ + X(Z + Y)(Z + Y)
XZ + X(YZ + Y Z) =
XZ + XYZ + X Y Z
Problem Solutions – Chapter 3
3-11. C
1
A
1
B
1 1 1
1
D F = AB + AC
3-13. AC
AB
AB
A D
a
ABD BCD ABC ACD ACDACD ABC ABC ABD ABCD
b
c
d
e
f
g
3-15. C 1 1 A
1 1
1
1 1
1
B
X X X X 1 1 X X
C 1 1
1
A
1
X X X X 1
C 1 1
B A
1 X X
1 1 1
1 1
X X X X 1
1
D
D
D
b = B + C D + CD
c=B+C+D
1
X X X X
A
X X
1
1
B
1 X X D
C 1 1
1
1
X X X X 1 1 X X
D e = B D + CD
1
B A
1
1
1
1 X X
1 X X X X
B
D
D
f = A + BD + BC + C D
g = A + CD + BC + BC
3-20. D3 0 X X X 1
D2 0 X X 1 0
D1 0 X 1 0 0
D0 0 1 0 0 0
A1 X 0 0 1 1
A0 X 0 1 0 1
V = D0 + D1 + D2 + D3
V 0 1 1 1 1
A0
A1
D2 X
1
1
1
D2 X
1 1
1
1
D3
A0 = D1 + D0 D2 A1 = D0 D1
2
1 D1
D1 D0
D0
B
d = ...