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Boolean Algebra
In order to help the pilot land, a particular aircraft’s autopilot
is connected to a device with four sensors. These sensors indicate
whether each of the following is favourable: the fuel on board, the
wind conditions (taking into account the wind speed and direction),
the angle of descent, and the state of the landing gear.
Based on the outputs of the four sensors, an alarm may or may not
sound. If the fuel is low or the landing gear is not engaged, the
alarm should sound; if this is not the case, unfavourable wind conditions
might be compensated for by favourable angle of descent, in which
case the alarm should not sound; otherwise, the alarm should sound.
Use the legend: A for fuel, B for wind, C for
landing gear, D for angle of descent (with 0 indicating unfavourable),
and F for the alarm (with 0 indicating no alarm).
(a) Construct a truth table for the device .[3]
(b) Obtain the Boolean expression from the truth table where the sensor
does not
sound. [2]
(c) Simplify using K-map to obtain the SOP and POS expression [5]
(d) Draw a properly labelled circuit diagram for the simplified expressions.
[4]
(e) Are your two circuits in part (iv) equivalent? [1]
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