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High definition programs are encoded with a type of resolution: 720p, 1080i or 1080p. The number stands for the amount of lines embedded within the signal. The letter describes the type of scan the television uses to display the picture. The "i" means interlaced and the "p" means progressive.
Why does the amount of lines matter?
The number of lines on a television is important because it allows for greater detail in the image. This is a similar concept to digital photos and how dpi determines print quality. The type of televisions all of us grew up watching had 480 visible lines on the screen. By doubling the amount of lines in combination with the type of scan, HD essentially doubles the quality of picture.
Does it matter if the resolution is interlaced or progressive?
The type of scan is arguable considering the amount of lines for each HD format. Progressive scan is a better type of scan because it doubles the amount of times the TV displays the image per one second in comparison to interlaced. Still, the difference between 720p and 1080i is so minimal that is isn't an issue at all. While 1080p is better than 720p and 1080i, very few programs are made in this resolution so it really isn't a factor right now.