Computer Science Grads who transitioned into Hardware roles

How did you do it?

Do you think a CS graduate would need a MS degree in ECE or CE to do so?

How would a CS graduate show employer proficiency in Hardware?

And by Hardware I mean everything a Computer Engineer is able to do.

I’m considering transferring to uOttawa from a semi-target school in the UK (from BSc Computer Science), because I want to focus on hardware. Either that or get a Masters ECE/CE somewhere like Georgia Tech after finishing CS