Would a DVI to HDMI adapter with a dvi cable have better quality than a regular DVI?

I currently have a VGA cable on my computer with a DVI-I can run in 1080p but I wonder if getting a DVI cable with an HDMI or vice verse would make me a better, my computer does no HDMI input, so therefore I wonder.

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    StarTech com Mini DVI to HDMI Video Cable Adapter for Macbooks

    KINAMAX 6 ft  HDTV DVI plug 24+5 to 3 x RCA Component Cable Adapter