BMP is a standard image file format which was historically used by computers running the Windows operating system. The format is more commonly know as Bitmap files. The term bitmap was originally coined in computer programming to refer to a map of bits. Historically when you saved an image on your home PC you might have saved it as a .bhp file, this is becoming less common with .jpeg the preferred image file format with the advent of digital cameras.
Bitmap files are housed in a device-independent bitmap (DIB) format. The term device independent means that the bitmap specifies pixel color in a form independent of the method used by a display to represent color. This enables Windows to show the bitmap on any type of display device - such as your monitor.
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PDF is a file format developed by Adobe Systems for representing documents in a manner that is separate from the original operating system, application or hardware from where it was originally created. A PDF file can be any length, contain any number of fonts and images and is designed to enable the creation and transfer of printer-ready output.
Each PDF file encapsulates a complete description of a 2D document (and, with the advent of Acrobat 3D, embedded 3D documents) that includes the text, fonts, images and 2D vector graphics that compose the document. They do not encode information that is specific to the application software, hardware, or operating system used to create or view the document.