Can I turn off power to some logic in my circuit and keep power on other logic?

Maybe not. If the part that is un-powered connects to outputs on the part that is powered, it may cause excessive drive current from the outputs that are powered. It may consume even more power than before.

Almost all modern logic chips have ESD (electrostatic Discharge) protection on the input pins. The protection consists of diodes to conduct negative input voltage to ground and conduct positive input voltage to VCC. The diodes only conduct if the voltage is out of range. If VCC is zero volts, any attempt to drive the input signal high will cause large currents to flow through the ESD diodes. This can damage the input of the un-powered logic and also damage the output of the logic that is powered on. That is why some chips get hot.

Therefore logic can only be powered off if its inputs are at ground or not driven (tristate).

This question has been closed by the EZ team and is assumed answered.