For the following logic expressions, create a corresponding truth table. Note that some terms in the logic expression may map to more than one place in the truth table. Note: The Boolean expression may need to be modified do to missing letters. Now that you understand the mechanics of converting from a truth table to a logic expression (and vice-versa), let’s look at a problem that begins with some written specifications. Your new car has an audio alarm that buzzes whenever the door is open and the key is in the ignition or when the key is in the ignition and the seatbelt is not buckled. Using the following variable names and assignment conditions, complete the truth table shown below that captures the functionality of this audio alarm. · D: Door → 0=Door Open / 1=Door Close · K: Key → 0=Key Not in Ignition / 1=Key in Ignition · S: Seat → 0=Not Buckled / 1=Buckled · B: Buzzer → 0=Buzzer Off / 1=Buzzer On D K S B (Door) (Key) (Seat Belt) (Buzzer) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Using the truth table you just created, write the un-simplified logic expression for the buzzer (i.e., variable B). Be sure that your answer is in the Sum-of-Products form.
. For the following logic expressions, create a corresponding truth table. Note that some terms in the logic expression may map to more than one place in the truth table. Note: The Boolean expression may need to be modified do to missing letters.
Now that you understand the
- Using the following variable names and assignment conditions, complete the truth table shown below that captures the functionality of this audio alarm.
|
· D: Door → 0=Door Open / 1=Door Close · K: Key → 0=Key Not in Ignition / 1=Key in Ignition · S: Seat → 0=Not Buckled / 1=Buckled · B: Buzzer → 0=Buzzer Off / 1=Buzzer On |
|
|
D |
K |
S |
B |
|
(Door) |
(Key) |
(Seat Belt) |
(Buzzer) |
|
0 |
0 |
0 |
|
|
0 |
0 |
1 |
|
|
0 |
1 |
0 |
|
|
0 |
1 |
1 |
|
|
1 |
0 |
0 |
|
|
1 |
0 |
1 |
|
|
1 |
1 |
0 |
|
|
1 |
1 |
1 |
|
- Using the truth table you just created, write the un-simplified logic expression for the buzzer (i.e., variable B). Be sure that your answer is in the Sum-of-Products form.
Step by step
Solved in 2 steps
