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pull up resistor is used to provide swing of the output till the positive supply.... pull down resistor for providing swing till the negative supply... there is a tradeoff involved between speed and power dissipation wrt the resistor value....
Pullups/ Pull downs are used on input lines.
An input line has to be high impedance other wise it would load the signal it is trying to monitor.
So if left open, it will float with no defined value.
It might even begin to oscillate, causing overheating and system crash.
A pullup/pulldown puts it in a well defined state, either high or low. It then needs a positive driving signal to make it change state.
IE: with a 10K pullup and a switch shorting the 10K to ground. You can then be sure if the switch is open or closed.