4K is the moniker used to describe a video resolution that has at least 4,000 horizontal pixels. There are a number of different 4K resolutions; a common one is 4096x2160, for a total resolution of 8,847,360 pixels - that's over four times the resolution of current 1080p
In the theatrical video realm, the move to digital cinema brought with it a need for higher-resolution video cameras and projectors, as well as a spec to help ensure that content creators, distributors, and exhibitors were all on the same page, quality-wise. Digital Cinema Initiatives, LLC (DCI) was formed in 2002 to develop a specification for mastering/playback of digital films in movie theaters. The DCI spec includes the option to master a film in either 2K (2048x1080) or 4K (4096x2160), and the spec further includes parameters for bit depth, color space, compression, and more.
4K requires expensive cameras and very powerful and high-resolution projectors to reproduce the resolution natively in the digital domain. 4k can be down-converted to 2k
and printed on 35-millimeter film for wide distribution to theaters that don't have 4k digital projectors.
While 4K technically requires at least 4,000 horizontal pixels, the more common trend in the A/V industry right now is to offer displays with a 3840x2160 resolutions This resolution was formerly called Quad Full HD because it is exactly four times the resolution of 1080p. However, in October 2012, the Consumer Electronics Association introduced the term "Ultra High-Definition" or "Ultra HD"
to describe any display device with at least 3840 horizontal pixels, 2160 vertical pixels, and an aspect ratio of at least 16:9. You can get more information on Ultra HD here
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