help with placing limit order on exchange

[anticonformist]

If i place a limit order to buy bitcoin (example 5400) and the current price is 5500, then what happens if i turn off my computer go to sleep then come back the next day, log back into the exchange and if the price did drop to 5400 while i was asleep, then will the exchange automatically execute my order?

[IIV]

Yes of course. That's why it's an online exchange.
It has nothing to do with your computer.