Notesale: Turn your study into money

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Question 1
In a test of learning potential, a scientist wishes to see how quickly a rat can learn to obtain
food from a dispenser when certain combinations of coloured lights are shown
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A rat is placed in a cage in which are three coloured lights, one red, one green and one blue
...
When certain
combinations of these lights are on, a food dispenser becomes active and the rat can obtain
food by pushing the door of the dispenser
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It is expected that the rat will
learn to push at the dispenser only when the correct lights are on
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All other
combinations will not provide food
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Draw a truth table representing each light as a Boolean variable, showing all
combinations of the variables and the output A which indicates whether the dispenser
is active or not
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Using the truth table, write down a Boolean expression that will activate the dispenser
when appropriate
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Use a Karnaugh Map to find the simplest representation of the expression
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Using the simplest expression, draw a circuit involving AND, OR and NOT gates which
could be used to operate the dispenser
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Red
T
T
T
T
F
F
F
F

Green
T
T
F
F
T
T
F
F

Blue
T
F
T
F
T
F
T
F

Output A
T
T
F
F
T
T
T
F

The truth table above shows when the combinations of colour lights that will enable the
dispenser to become active or inactive,the T stands for true which means the light is on or
will provide food and false means the lights are off or will not provide food
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2
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rgb + rgb’ + r’gb + r’gb’ + r’g’b =gb(r+r’)+gb’(r+r’)+r’g’b
=gb
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1+r’g’b
Output A =gb+gb’+r’g’b=>g+ r’g’b

3
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r

g’

g

g
1

g’

1

r’
1

Region 1

1

1
Region 2

b’

b

b’

b
Above is my kirnaugh map of my Boolean expression and below is the Boolean expression
simplified by using the Karnaugh map
...
This is my switch circuit that shows how the simplified expression works
r’

r
b

g’r’b

b
g’

g
Output A=g+ g’r’b

g

A



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