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Why not on my Nexus 7?

If you use a Nexus 7, you probably have a Google account, so you could use a Google Voice number to register.

Google Play doesn't make it available to the Nexus 7 (at least, I don't see it on mine).

It uses an SMS to register your phone number.

You can send the verification call/text to any old phone and type it in on the Signal device.