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I am trying to build a half adder using a 74LS86 XOR gate. Initially I connected both input pins that I am using (9 & 10) on the 74LS86 to the ground rail using 10K ohm resistors. I then connected 5V to pin 9 and expected the LED fed from pin 8 to light. No luck. I then pulled pins 9 and 10 high by connecting the 10K ohm resistors to 5V. When I pulled pin 10 low by connecting it to ground, the LED lit. I substituted 330 ohm resistors for the 10K resistors and reconnected them to ground. Now the circuit works properly when I pull either pin 9 or 10 high. Is 330 ohms an appropriate choice? Are pins 9 and 10 sourcing current when they are not active (pulled high)? I read that low power schottky ICs can only source 8mA. I am calculating that with 5V and 330 ohms that the current draw could be 15mA. I am wondering where I should look on the datasheet to properly size pulldown resistor for TTL ICs. 74LS86 Datasheet:https://www.apogeeweb.net/circuitry/74ls86-xor-gate-digital-ic-2--simple-using-and-other-information.html

You should not need a pullup or pulldown resistor with a logic gate, when the output goes from a logical 1 to a logical 0: the gate is able to sink the current.

You must use a resistor to limit the current through a LED (or use a constant current sub-circuit). Some LED becomes visibly turn on with 20 mA, in sun light, others with just 5 mA, in a poorly lighted room. With a 10k resistor, assuming you are using 5V, that leaves a current way too small to turn the LED on (to the naked eye).

Have you look at the many videos by Ben Eater on Youtube? Four bits adder, Ben Eater