• The basic types of discrete logic problems are,

1. Conditional - if a set of conditions can directly cause an action.

e.g. if the temperature is too high and there is an ingot in only one bay, turn on fan 1.

B1 = bay 1 ingot detect

B2 = bay 2 ingot detect

F1 = fan 1

T1 = temperature overheat sensor


in Boolean F1 = T1 * (B1 EOR B2)

or F1 = T1 * (( B1 * B2 ) + ( B2 * B1 ))

or F1 = T1 * B1 * B2 + T1 * B2 * B1


In ladder logic,



2. Sequential - when the system is in a certain state, the controls will do certain things.

e.g., when an oven is on, the PLC adjusts temperature.When it is off doors can be opened/closed.






• Try the example shown below,



• Consider the more complicated design that follows,






1.2.1 Boolean Algebra for Circuit and Ladder Logic Design


• When we have logical decisions to make, truth tables and Boolean algebra allow formal methods to be used. The use of formal methods improves the overall quality of the design.


• Consider the example of a burglar alarm

1. If alarm is on, check sensors.

2. If window/door sensor is broken (turns off), sound alarm and turn on lights

3. If motion sensor goes on (detects thief) sound alarm and turn on lights.


A = Alarm and lights switch (1 = on)

W = Window/Door sensor (1 = OK)

M = Motion Sensor (0 = OK)

S = Alarm Active switch (1 = on)







• This example was quite simple. To do more complicated problems we will need to review some basic theory first.



1.2.2 Boolean Forms


• Canonical, truth tables