karnough map

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