1.2 DISCRETE LOGIC
• 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