1080p/24 is a resolution and framerate indicative of Hollywood movies on Blu-ray discs. 1080p is the resolution, implying a full HD resolution of 1,920 by 1,080 pixels. The "P" stands for "Progressive." which means each frame has all the pixels listed. This is the opposite of "i" or "interlaced" which shows half the horizontal lines each frame. The 24 is the number of frames per second in the video. The most common framerate for video is 60, or 60 Hz, which is 60 frames per second. 24 is how many frames nearly all Hollywood movies are shot at.
The importance of 1080p/24 is as an output for Blu-ray and upconverting DVD players. This means the player is able to output the movie without adding anything additional to the image. If one has a TV with an adjustable framerate (i.e. 72 or 96) instead of the normal 60, 1080p/24 video can be displayed in a smooth multiple. 120 Hz and 240 Hz TVs generally also have this ability.
If a TV is 60 HZ, or isn't able to accept a 1080p/24 signal, the 24 frames per second of films need to be converted in a process called "3:2 Pulldown" that shows the first frame of video twice, the second frame three times, the third frame twice and so on, so there are frames to show 60 times per second. This can create a noticeable judder that is absent with TVs that can display some multiple of 24 (showing 1080p/24 material).
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