Hello,

What I'm missing is if the 74LS02 is a fixed requirement, or if there is an 
option to use the 3.3V sibling. Thus shifting the problem to the xx74xx02 
inputs. Because if you kill the 74LS02 with your experiments it might hurt 
less than if you kill the BBB.

I would NOT use current limiting resistors, I don't thing that they 
> solve the problem. 
>
This has been done for decades. I don't see why  it should not work for the 
Sitara.
If the I/O voltage is 3.3V and we assume the clamping voltage 0.3V the 
overvoltage is 5V-3.6V = 1.4V. As an indication of  clamping diode 
capability can we take the pin current capability. Eg. 4mA (varies over 
pins). Than we would only need a 350Ohm series resistor. -> Take 10k and 
you cover all the wrong assumptions ;-).
You can take even higher resistors (eg. 100k). But you will limit your 
maximum frequency because somewhere you will not charge the capacity of the 
Sitara input buffers fast enough. High resistors values can also increase 
EMC susceptibility.

Further more pins USB0_VBUS and USB1_VBUS should withstand 5V. But I assume 
you need USB and you need 4 inputs.

Chilli


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