Does updating to ios 7.0.4 diminish my space on my new iPhone 5s?

I just bought a brand new iPhone 5s and have an update already to install ios 7.0.4. I have a 16 gig capacity on the phone itself.  Does installing ios 7.0.4 take up any of my 16 gigs?  Or does it "swap" for the ios 7.0.3 that is already "built in" to the phone?  I'm always concerned about updates taking up more space than the old version and would like some clarity on this. Thanks very much!

It would depend on how many changes there are to the software (primarily new features).
Updates always replace existing code but could be larger (in total size) if thay have added functionality.
Minor updates like 7.0.x represent just changes to the software and are (usually) quite small to download.

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