Automating Manufacturing Systems - Process Control and ...

plc boolean - 6.8
Ladder Logic for Equation (3):
B1
B2
T
F
B1
B2
T
Figure 6.6
Alternate Ladder Logic
Boolean algebra is often used in the design of digital circuits. Consider the example
in Figure 6.7. In this case we are presented with a circuit that is built with inverters,
nand, nor and, and gates. This figure can be converted into a boolean equation by starting
at the left hand side and working right. Gates on the left hand side are solved first, so they
are put inside parentheses to indicate priority. Inverters are represented by putting a NOT
operator on a variable in the equation. This circuit can’t be directly converted to ladder
logic because there are no equivalents to NAND and NOR gates. After the circuit is converted
to a Boolean equation it is simplified, and then converted back into a (much simpler)
circuit diagram and ladder logic.
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