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I was doing some simple arduino project which was involving the knowledge of logic gates.So I first thought of dealing with logic gates before doing the project and came to know about the pull up and pull down resistors.and my question is "Is the circuit possible without using pull up and pull down resistors?What will be the outcome of glowing leds using simple AND or OR gate without using pull up and pull down resistors?"
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You should only need pull-up resistors when you have Open Collector outputs (basically an NPN transistor).

You have to look at the datasheet for your particular logic family to see if they can source enough current to light an LED.  For example the 74LS08 Quad 2-input AND gate (http://www.ee.washington.edu/stores/DataSheets/74ls/74ls08.pdf) can only source 0.8 mA, not enough to light an LED, but it can sink up to 16 mA so you can connect the LED backward (+5V / resistor / LED / pin) and have the LED come on when the pin goes LOW.
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Quote
"Is the circuit possible without using pull up and pull down resistors?
What circuit?

Quote
What will be the outcome of glowing leds using simple AND or OR gate without using pull up and pull down resistors?
Pull up or down resistors where?

In general you would only use pull up resistors with 74LS logic as the value you need for pull down resistors is too small. Pull up 4K7 pull down 330R.
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Most logic gates have what is known as "push-pull" or "totem-pole" outputs, meaning they either drive HIGH or drive LOW
and never "float".

Open-collector (or more often these days open-drain) gates are usually only used for specific reasons including:

o Permiting the circuit you are driving to use different voltage to the logic supply - most open-collector gates allow
   higher than 5V for instance, and you can interface between 3.3V and 5V this way.
o Robustness - if the output is shorted to ground nothing bad can happen - often sensors are open-collector for these two
   reasons.

o Allowing wired-and gates to be formed from several open-collector outputs connected together and sharing a pull-up.
o Driving a databus when there are other output devices connected to it - open-collector outputs prevent electrical
   contention (there can still be logical contention for the bus but no magic smoke can be released) - this is really an
   application for the wired-and gate just mentioned.
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