| 3. |
(a) The following diagram shows an
automobile alarm circuit that is used to detect certain undesirable conditions. The three
switches are used to monitor the status of one of the doors, the ignition system, and the
headlights. |
|
|
 |
|
|
Design a logic circuit that takes
these three switches as inputs and activates the alarm when, and only when, either of the
following conditions exists: |
|
|
|
the headlights are on and the ignition is off |
|
|
|
the door is open and the ignition is on |
|
|
Your answer should
consist of: |
|
|
(i) a truth table |
[4] |
|
(ii) a complete K-map |
[2] |
|
(iii) a simplified SOP expression |
[2] |
|
(iv) the logic diagram itself |
[2] |
|
|
|
|
(b) Consider the circuit shown
below: |
[5] |
|
 |
|
|
Using Boolean algebra,
show how the number of gates in the circuit can be minimized. Draw the logic diagram for
the minimized circuit. |
|
|
|
|
|
(c) Show how a NAND gate can be
implemented using only multiplexers. Draw a block diagram to illustrate your
answer, labelling all of the inputs and outputs clearly. |
[5] |