Newbie Question - Help Please

I am developing a circuit and want to do something that I think is relatively simple. I am very much a novice at designing my own circuits. I have taken pieces from other circuits and adapted them to my own use. On my current project, I want to have an automatic power supply switch.

Meaning, under normal conditions I would run off of a 9V battery throuh a power regulator to +5V to drive my circuit. However, in cases where my battery diesor I want to preserve it, I want to be able to run off of a +5v Power adapter.

What do I do circuit wise to provide an automatic switch that senses when the adapter is plugged in and does not draw power from the battery.

I have doen several searches, and probably do not have the right terminology for this to provide an accurate result.

Many thanks appreciated!!

Added after 1 hours 34 minutes:

Oops.. I think I posted this in the wrong section.

Mods, please close and I will re-post in the Elementary section.

I think that full power-off and re-on automatically can't be acheived, but you may be able to obtain very low drawn current from the supply as if you are in the sleep mode..
but zero drawn current w/o external additional supply (or even a battary) may be logically impossible.

Hope that helped,
Regards,
Ahmad,

You want to Save power or switch off when your battery is not working but remember there would be some µA flowing in the Circuit because of Active elements in the Circuit.
But it is negligible use the sencor which do not sense this current