ECE 201; HW solutions for 3rd Edition; Chapter 2

P1

x y z
x+y+z
(x+y+z)｢
x｢y｢z｢
xyz
(xyz)｢
x｢+y｢+z｢

0 0 0
0
1
1
0
1
1

0 0 1
1
0
0
0
1
1

0 1 0
1
0
0
0
1
1

0 1 1
1
0
0
0
1
1

1 0 0
1
0
0
0
1
1

1 0 1
1
0
0
0
1
1

1 1 0
1
0
0
0
1
1

1 1 1
1
0
0
1
0
0

P2

a

xy + xy｢ = x(y+y｢) = x(1) = x

b

(x+y)(x+y｢) = x + yy｢ = x + 0 = x

c

xyz + x｢y + xyz｢

xy(z+z｢) + x｢y

xy + x｢y = (x+x｢)y = y

0.1 d

(A+B)｢(A｢+B｢)｢

A｢B｢AB = AA｢BB｢

P4

a

A｢C｢+ ABC + AC｢

(A｢+A)C｢+ ABC

C｢+ ABC

(C｢+C)(C｢+AB)

C｢+ AB

0.2 b

(x｢y｢+z)｢+ z + xy + wz

(x｢y｢+z)｢+ z + xy by absorption

(x+y)z｢+ z + xy by DeMorgan's

((x+y)+z)(z｢+ z) + xy

x+y+z + xy

x+y+z by absorption

c

A｢B(D｢+C｢D)+B(A+A｢CD)

B[A｢(D｢+C｢D)+(A+A｢CD)]

B[A｢(D｢+C｢)(D｢+D)+(A+A｢)(A+CD)]

B[A｢(D｢+C｢)+ A+CD]

B[A｢D｢+A｢C｢+ A+CD]

B[A｢D｢+(A｢+A)(C｢+A)+CD]

B[A｢D｢+C｢+A +CD]

B[A｢D｢+ A + (C｢+C)(C｢+D)]

B[A｢D｢+ A + C｢+D]

B[(A｢+ A)(D｢+A) + C｢+D]

B[D｢+A + C｢+D]

B(A + C｢+ 1)

B(1) = B

P6

Find the complement of the following expressions:

a

(xy｢+x｢y)｢ = (x｢+y)(x+y｢)

b

((AB｢+ C)D｢+E)｢

((A｢+B)C｢+D)E｢

c

[ (x+y｢+z)(x｢+z｢)(x+y) ]｢

x｢yz｢+ xz + x｢y｢

P8

List the truth table of the function:

F = xy + xy｢+ y｢z

x
y
z
F

0
0
0
0

0
0
1
1

0
1
0
0

0
1
1
0

1
0
0
1

1
0
1
1

1
1
0
1

1
1
1
1

P14

*

a (xy+z)(y+xz)

F = S(3,5,6,7)

F = P(0,1,2,4)

b

(A｢+B)(B｢+C)

F = S(0,1,3,7)

F = P(2,4,5,6)

c

y｢z + wxy｢+ wxz｢+ w｢x｢z

F = S(1,3,5,9,12,13,14)

F = P(0,2,4,6,7,8,10,11,15)

P15

F = xy｢z + x｢y｢z + w｢xy + wx｢y + wxy

a

w
x
y
z
F

0
0
0
0
0

0
0
0
1
1

0
0
1
0
0

0
0
1
1
0

0
1
0
0
0

0
1
0
1
1

0
1
1
0
1

0
1
1
1
1

1
0
0
0
0

1
0
0
1
1

1
0
1
0
1

1
0
1
1
1

1
1
0
0
0

1
1
0
1
1

1
1
1
0
1

1
1
1
1
1

F = xy｢z + x｢y｢z + w｢xy + wx｢y + wxy

F = (x+x｢)y｢z + (w｢+w)xy + wx｢y

F = y｢z + xy + wx｢y

F = y｢z + (x + wx｢)y

F = y｢z + (x + w)y

P16

F(A,B,C,D) = B｢D + A｢D + BD

F = (A+A｢)B｢(C+C｢)D + A｢(B+B｢)(C+C｢)D + (A+A｢)B(C+C｢)D

F(SOM) = A｢B｢C｢D + A｢B｢CD + AB｢C｢D + AB｢CD + A｢B｢C｢D + A｢B｢CD + A｢BC｢D+ A｢BCD + A｢BC｢D + A｢BCD + ABC｢D + ABCD

F(SOM) = S(1,3,5,7,9,11,13,15)

F(POM) = P(0,2,4,6,8,10,12,14)

File translated from T_EX by T_TH, version 2.86.
On 17 Sep 2001, 08:54.