MAE 2055: Mechetronics I
Mechanical and Aerospace Engineering
Fall 2013
Homework 9
In this homework you will design a digital circuit whose output is an enabling signal for a pushbutton
ignition system in an automobile. When the output of this circuit is high, the starter is enabled, and
pushing the start button will start the car.
The start enable output signal should be high (S = 1) when all of the following three conditions are true:
•
•
•
The engine is not already running
The clutch is depressed
The emergency brake is on or the footbrake is depressed
A block diagram of the circuit is shown below. Assume that the inputs come from sensors that detect
the state of the engine, the clutch, and the brakes. The inputs are:
•
E
E = 1 if the engine is running
E = 0 if the engine is not running
•
C
C = 1 if the clutch is depressed
C = 0 if the clutch is not depressed
•
EB
EB = 1 if the emergency brake is on
EB = 0 if the emergency brake is off
•
FB
FB = 1 if the footbrake is depressed
FB = 0 if the footbrake is not depressed
The output is a signal that enables the starter solenoid:
•
S
S = 1 – the starter is enabled
S = 0 – the starter is disabled
E
C
EB
FB
Digital
Circuit
S
1) Generate the truth table for this circuit. You can simply fill in the output values in the truth table on
the following page. Attach the completed truth table to your homework.
2) From the truth table generate the complete sum-of-products (SOP) logic expression for the circuit.
3) Draw the SOP logic circuit corresponding to the expression you just derived. You may use the
partially-drawn circuit on the following page. Simply make the appropriate connections between the
inputs and the AND gates to generate the correct minterms. Label the minterm at the output of
each AND gate. Attach the completed schematic to your homework.
4) While the complete SOP circuit implementation will produce the desired output, it is far from being
a minimized logic circuit. That is, the same functionality can be achieved using far fewer gates.
Using the rules and identities of Boolean algebra, simplify the SOP expression to a form that will
require fewer logic gates. You should be able to implement the circuit with two AND gates, one OR
gate, and one inverter. Refer to the Section 8 notes on the website for a list of Boolean algebra rules
and identities.
The following procedure may help you simplify the expression:
a) Factor out the common variables from each minterm (i.e., E� ∙C).
b) Factor out one term from two of the other minterms (e.g., EB), then apply the Boolean
� = 1.
identity A+A
c) Apply the identity A∙1 = A.
d) Apply the identity �
A∙B + A = A + B.
Show the details of each step you take in getting to the simplified expression.
5) Draw the logic circuit corresponding to your simplified expression. You should be able to reduce
your circuit to two AND gates, one OR gate, and one inverter. You will be building this circuit in the
lab next week.
Look at the resulting simplified circuit, and read the requirements for the circuit on the previous
page again. This is probably the circuit you would have come up with if you had just designed it
directly from the list of requirements.
Truth table for question #1:
E
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
C
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
EB
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
FB
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
S
SOP circuit for question #3:
E
C
EB
FB
Write the minterms at the
output of each AND gate.
S