Resistor Heating up in AND gate
You didn't say what your "right voltage" is and you didn't give a schematic. There's a schematic editor included on top of the editor box. Use it!

10Ω is a very low resistor value for limiting an LED current (that's what I think you are trying to do), you may burn a few watts on that resistor. Most likely, it's too small. Or your resistance is calculated wrong.