Standard definition means 480i.
That alone answers your question.
You can't get 1080 in a 480 TV.
Although 'resolution is used for many things, the acronym DPI doesn't apply in this case. The DPI (dots per inch) is for printing, where dots form the halftones of inks on paper.
PPI (pixels per inch, what is usually called DPI) of each TV would be different depending on size of screen. The bigger the screen, the lesser the DPI. The math is vertical pixels/vertical inches, i.e. 480/24 = 20DPI. That's in normal zoom mode. If zoom is used, you have to figure out how many pixels your TV is not showing at top and bottom, and assume your vertical pixels shown are, lets say 400.
In any case, even if your TV is HD, you'll be losing a good portion of image when using any zoom setting other than normal (having black bars at left and right) because your TV will be assuming you are putting legacy systems signal in the video input.