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E

C

An inexpensive PLC is worth X B A at least a few hundred dollars

C Consider the cost trade-off!

Figure 6.8 A Boolean Equation and Derived Circuit and Ladder Logic

The initial equation is not the simplest. It is possible to simplify the equation to the form seen in Figure 6.8. If you are a visual learner you may want to notice that some sim plifications are obvious with ladder logic -consider the C on both branches of the ladder logic in Figure 6.9.

plc boolean -6.12

CE

A = B ??(D ++ F )

Figure 6.9 The Simplified Form of the Example

The equation can also be manipulated to other forms that are more routine but less efficient as shown in Figure 6.10. The equation shown is in disjunctive normal form -in simpler words this is ANDed terms ORed together. This is also an example of a canonical form -in simpler terms this means a standard form. This form is more important for digital logic, but it can also make some PLC programming issues easier. For example, when an equation is simplified, it may not look like the original design intention, and therefore becomes harder to rework without starting from the beginning.

plc boolean -6.13

C

A = (B ??D)+ (BCE)+ (BCF)

Figure 6.10 A Canonical Logic Form

6.3.1 Boolean Algebra Techniques

There are some common Boolean algebra techniques that are used when simplifying equations.

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