karnough map
DESCRIPTION
mechatronicsTRANSCRIPT
Chapter - Karnaugh Maps
These allow us to simplify without Boolean algebra
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.
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
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+ =
Example (create logic using a Karnaugh map)
A B C D Result
0101010101010101
0011001100110011
0000111100001111
0000000011111111
1001010110010011