Solution Manual Chapter 9: Logic and Computers
9-1. A popular ditty of the late nineteenth- and early twentieth-century railroad era was
the following (Sung to the tune of “Humoresque” by the nineteenth-century Czech
composer Antonin Dvorak1):
“Passengers will please refrain – From flushing toilets – While the train – Is
standing in the station – I love you.”
For the preceding ditty, define a variable S expressing whether or not the train is in the
station, a variable M expressing whether or not the train is moving (“standing” means
“not moving”), and a variable F expressing the fact that the toilet may be flushed. (A: S =
“the train is the station,” M = “the train is moving” (or you could use its negation,
M′ meaning the train is stationary), and F = “the toilet may be flushed”)
Need: S = “____”, M = “______ “, and F = “ _____”.
1 You can find the music at: http://www.youtube.com/watch?v=_93anoTqIgU
9-2) For the ditty in Exercise 9-1, a) express the ditty as a logic formula for the
conditions under which one may flush the toilet, b) evaluate the formula you wrote in a)
for M = 1 and S = 1 and c) express in words the meaning of your answer to b). (Assume
that any behavior not explicitly forbidden is allowed.)
Need: F = ? (a combination of the variables M and S with the symbols
chosen from among +, ‘, & •)
Know: S = “the train is the station”, M = “the train is moving” and F =
“the toilet may be flushed”.
9-3. Rework Example 9-2 to express and evaluate the logic formula to answer the
question “If the speed is below the set speed and the set speed is above the speed limit,
then will the throttle be opened?”
Need: A binary logic formula expressing the statement, “If the speed is
below the set speed and the set speed is above the speed limit, then will
the throttle be opened?”
9-4. In Example 9-3, include the additional Boolean variable that for actuation of the
warning light the driver’s door must be closed (Ddoor is true if the driver’s door is closed).
Need: A Boolean expression for the truth of the statement “W = the seat belt
warning light should be on in my car,” using all of the following Boolean
variables:
D is true if the driver seat belt is fastened.
Pb is true if the passenger seat belt is fastened.
Ps is true if there is a passenger in the passenger seat.
Ddoor is true if the driver’s door is closed.
9-5. Consider the following logic variables for a car:
Db = “the driver’s seat belt is fastened”
Pb = “the passenger seat belt is fastened”
W = “the seatbelt warning should be on in my car”
Write a sentence in English that expresses the logic equation W = Db′ + Pb′. (A: W = “If
either the driver‘s seat belt is not fastened or the passenger’s seat belt is not
fastened, the seatbelt warning light should be on.”)
Need: Translation into English of the statement W = ______?
9-6. Consider the following logic variables for a car:
W = “the seatbelt warning light is on”
D = “a door of the car is open”
Ps = “there is a passenger in the passenger seat”
K = “the key is in the ignition”
M = “the motor is running”
Db = “the driver’s seat belt is fastened”
Pb = “the passenger seat belt is fastened”
Write a logic equation for W that expresses the following sentence:
“If all the doors of the car are closed, and the key is in the ignition, and either the driver’s
seat belt is not fastened or there is a passenger in the passenger seat and the passenger’s
seat belt is not fastened, then the seatbelt warning light should be on.”
Need: W = ?
Know: Statements for D, Ps, K, Db,& for Pb
9-7. Consider the following logic variables for a car:
M = “the motor is running”
Db = “the driver’s seat belt is fastened”
In the early 1970s Congress ordered all seat belt warnings to be tied to the motor in a
manner expressed by the following sentence. “If the driver’s seat belt is not fastened then
the motor cannot be running.”
a) Suppose the car is in proper working condition and the driver has just turned the key.
Write a logic equation for M in terms of Db that expresses the sentence in quotes above;
b) write a truth table for that logic equation
Need: Translation of edict “If the driver’s seat belt is not fastened then the
motor cannot be running” into a logic statement and a truth table.
9-8. Consider the following logic variables:
A = “a customer at a restaurant orders an alcoholic beverage”
I = “the customer shows proper identification”
M = “a customer at a restaurant is over 21”
Consider the sentence “If a customer at a restaurant is over 21 and shows proper
identification then she can order an alcoholic beverage.” a) Express this sentence as a
logic equation, b) write a truth table for the logic equation.
Need: A = _________?
Know: Definitions of statements A, I and M.
9-9. Consider the following variables expressing a football team’s strategy.
T = “It is third down”
L = “We must gain more than 8 yards to get a first down”
P = “We will throw a pass”
The team’s strategy is expressed by the following truth table
.
Write a logic equation for P in terms of T and L.
Need: P = ?
Know: Defining statements for T, L, and P.
T
L
P
0
0
0
0
1
1
1
0
1
1
1
1
9-10. Consider the following electric circuit
Consider the variables L = “the light is on”, A = “switch A is closed” and B = “switch B
is closed.” Express the relationship depicted by the electric circuit as a logic equation for
L in terms of A and B.
Need: L = ?
AB
L
9-11. Consider the following circuit diagram and the variables L = “the light is on”, A =
“switch A is closed” and B = “switch B is closed,” and C = “switch C is closed”.
Write a logic equation for L in terms of A, B, and C.
Need: L = ?
A
L
BC
A
L
BC
9-12. Consider the following logic variables for a car:
W = “the seatbelt warning light is on”
Ps = “there is a passenger in the passenger seat”
Db = “the driver’s seat belt is fastened”
Pb = “the passenger seat belt is fastened”
Draw a circuit diagram for the logic equation W = Db‘ + (Ps • Pb‘)
Need: Circuit diagram = Picture with W, Db, Ps, and Pb
9- 13. Explain the following sentences.
a) “There are 10 kinds of people in the world, those who understand
binary numbers, and those who don’t.”
b) “Binary is as easy as 1, 10, 11.”
Need: Convert simple binary numbers to familiar decimals to make idiomatic
sense of question..
9-14. Convert the following numbers from binary to decimal: (a) 110, (b) 1110,
and (c) 101011. Partial A:
—
25
24
23
22
21
20
Decimal
equivalent
—
32
16
8
4
2
1
—
a) 110
0 32
0 16
0 8
1 4
1 2
0 1
6
b) 1110
c)101011
Need: 110 = ____? (a decimal number), 1110 = ____? (a decimal
number), 101011 = _____? (a decimal number)
Know:
25
24
23
22
21
20
32
16
8
4
2
1
0 32
0 16
1 4
1 2
0 1
9-15. Convert the following numbers from decimal to binary: (a) 53, (b) 446, and (c)
1492.
Partial A:
Decimal
1024
512
256
128
64
32
16
8
4
2
1
Binary
place
210
29
28
27
26
25
24
23
22
21
20
a) 53
0
0
0
0
0
1
1
0
1
0
1
b) 446
c) 1492
Need: a) 53 in binary = ______?, b) 446 in binary = ______? & c) 1492
in binary = _____? (each answer a sequence of 1s and 0s)
Know:
1024
512
256
128
64
32
16
8
4
2
1
210
29
28
27
26
25
24
23
22
21
20