not: lets say, you have a float in your basement that is nc (normally closed, like a light switch turned on, when not under water). you want to use this float for an alarm. if you wire this float directly to the alarm panel it will be on when the basement is dry! therefore we reverse the incoming signal to the alarm panel through a not gate. consequently; 0=1, and 1=0, so the alarm will only sound when your feet are wet.
or: lets say, you have a large basement with two water infiltration areas, and also two float switches wired no (normally open, like a light switch off when dry). we really don't care which area has water when we are asleep, we just want to know that there is a problem. therefore; we require an alarm whether float # 1 OR float # 2 is under water, and consequently apply these float signals to an OR gate for an alarm.(0 with 0 input=0 output feet dry/no alarm, 0 with 1 input=1 output, feet wet/ alarm, 1 with 0 input= 1 output, feet wet alarm.
and; lets say your dog runs away through two doors every time they are both open at the same time.
we will place a no switch on each door, so that an alarm will sound every time both doors are open, using an AND gate. [0 with 1 input = 0 dog ok & no alarm, 1 with 0 input = 0 dog ok & no alarm, 1 with 1 input = 1 dog may be run over & alarms go off like gang busters (whatever that is) so you to save him/her from peril]