Boolean algebra and digital circuit

Boolean algebra is often used in the design of digital circuits. Consider the example in Figure below. 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.

The circuit is converted to a Boolean equation and simplified. The most nested terms in the equation are on the left hand side of the diagram.

 This simplified equation is converted back into a circuit and equivalent ladder logic.

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