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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PNG pronounced ping is a format for storing bitmapped (raster) images on computers. It was created originally to replace the GIF file format when it was announced that the companies who created the GIF format wanted royalties. PNG uses indexed colors and lossless compression (like a .GIF file), but without those copyright limitations; it cannot be animated like a GIF image.
PNG images are in many ways better than .GIF as they also include an 8-bit transparency channel, which allows the colors in the image to fade from opaque to transparent; GIF images only support fully opaque or fully transparent pixels. PNG supports palettes of 24-bit RGB colors, RGB images or greyscale or RGB images. PNG was intended to be able to transfer images on the Internet, not professional graphics, and so does not support other colour spaces (such as CMYK).
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