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I'm controlling three 4066 (Quad Bilateral Switch) with two chained 74HC595 (8-bit serial-in, serial or parallel-out shift register with output latches; 3-state)

Do I need to use pull up resistor with the 4066 in that cas ? I can't found on the web or datasheet application with them. So do I need to put a grounded resistor connected betwwen the 74HC595 outputs and the associated 4066 inputs ?

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The default type for logic output drivers is push-pull. This actively pushes the voltage up when the output is high, and pulls it down when the output is low. There is usually no need for further resistors tied to either supply.

The exception would be when the output driver cannot source enough current to drive its load but can sink more than enough, or vice versa with the resistor tied to the "weak" supply in order to assist the driver. But 74HC devices usually have a decent amount of current available for actively driving a load.

Only when the output driver is open drain are pull-up resistors required, whether discrete or integrated into an IC. Tri-state outputs are usually connected together and no fewer than (and usually only) one output active in order to prevent the input they are connected to from floating.

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