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How is it possible to have a the same output address in the input address and what would be the Boolean expression and truth table?

 

Perhaps this will help.

https://instrumentationtools.com/plc-latching-function/

I found that by just Googling "boolean ladder logic".

 

The Y label on the right represent the relay coil.
The Y label on the middle branch represents one "normally open" set of relay contacts associated with coil "Y". When coil "Y" is energized, all of it's "normally open" contacts are closed. This structure is often referred to as a "sealing contact". It is similar to a traditional latch. Once "energized", coil Y will remain in that state until the "normally closed" contact A becomes open, interrupting current flow through coil Y.

In Boolean terms this would be:

MOD NOTE: Answer removed.

Remember, Homework HELP, not Homework Done For You!

 

Thank you for all the help. As for a ladder logic diagram, would I use the same output address, for the Y in the separate rung? In the simulator, when the logic level of NO is true, the coil Y doesn't become energized and thus my output doesn't become energized.

 

I'm not sure I understand your question. With the rung you have drawn you need contact A, normally closed to be true AND contact B normally open to be true, then coil Y will be energized and normally open contact Y will be true. This allows normally open contact B to be true or false without de-energizing coil Y. Normally closed contact A must be false for coil Y to be de-energized. If you are talking about another rung then you need to draw it.