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I am a bit lost looking at the current information of the datasheet of the SN54HC595.

What do the 3 current parameters (Ii, Ioz, Icc) mean? I've tried to find the description of them in the rest of the datasheet but couldn't find it.

I think Ioz is the high impedance one, but what Vo=Vcc means as its test condition?

Finally, what about Ci (bottom row)? Does 'i' stands for input? If so, are they suggesting to place it between Vcc and GND?

Electrical characteristics of the component

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Ii is the input current for any input, over an input voltage range of 0 V to Vcc.

Ioz is the output leakage current when the outputs are tri-stated. Since these outputs can be connected to the outputs of other devices (which is the reason the are tri-statable), the other device could apply a voltage to that output pin. These outputs could also be connected to a pullup or pulldown resistor which could apply 0 V or Vcc to the output when it is tri-stated. So the output leakage current is specified over a voltage range, 0 V to Vcc in this case (just like the inputs).

Ci is the input capacitance of the specified pin, when it is not connected to anything. This parameter is needed when calculating the maximum capacitance on the driving net.

And no, the manufacturer is not suggesting that you add a capacitor to the input pin.

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The test conditions for Ioz mean "If an output pin is in the high-impedance state and you connect an external voltage source to that pin and you set the value of the source to either 0 or Vcc, then the current through the source will not exceed the maximum specified Ioz."

Ci is characteristic of the input; that's how much capacitance you would see if you measured the input capacitance.

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