Download - karnough map
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Chapter - Karnaugh Maps
These allow us to simplify without Boolean algebra
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Another Example Case
The inputs and outputs are chosen to be;
A = Alarm and lights switch (1 = on)W = Window/Door sensor (1 = OK)M = Motion Sensor (0 = OK)S = Alarm Active switch (1 = on)
The basic operation of the alarm can be described with rules.
1. If alarm is on, check sensors.2. If window/door sensor is broken (turns off), sound alarm and turn on lights3. If motion sensor goes on (detects thief) sound alarm and turn on lights.
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Karnaugh Maps (setting up the maps)
Given
A, W, M, S as beforeQ = Alarm Quiet ( 0 = quiet )
Step1 : Draw the truth table
S M W Q A
0000000011111111
0000111100001111
0011001100110011
0101010101010101
0000000001000101
Step 2 : Divide the input variables up. I choose SQ and MW
Step 3 : Draw a Karnaugh map based on the input variables
MW (=00) MW (=01) MW (=11) MW (=10)
SQ (=00)SQ (=01)SQ (=11)SQ (=10)
1 1 1
Added for clarity
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Karnaugh Maps (converting them to logic)
Step 4 : Look for patterns in the map
MW MW MW MW
SQSQSQSQ
1 1 1
M is the common term
W is the common term
all are in row SQ
M S AQ
W
Step 5 : Write the equation using the patterns
Step 6 : Convert the equation into ladder logic
A S Q M W+ =
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Example (create logic using a Karnaugh map)
A B C D Result
0101010101010101
0011001100110011
0000111100001111
0000000011111111
1001010110010011