A PSD file is known as a Photoshop document and was developed by Adobe in order for Graphic Designers to create layered images. PSD is the propiertry format that Adobe uses to allow these files to be saved in, they can then be either opened in various versions of Adobe Photoshop or if a user wants to send them to others they can be flattened to PNG, JPG or other more standard image formats. You can't however re-convert a JPG/PNG file that has been converted from a PSD back to a PSD file - it loses it's layers.
Photoshop files have the .PSD file extension, this PSD stores an image with support for a lot of imaging options such as Masks, transparency, clipping paths and duotone settings. Sometimes Photoshop files have the extension .PSB which essentially stands for Photoshop Big, this allows images to support up to a maximum height and width of 300,000 pixels and a length limit of 4 Exabytes.
The GIF file format is a type of bitmap image and has become popular due to the growth of the internet. This file format supports up to 8 bits per pixel therefore giving an image the ability to contain 256 distinct colours chosen from the 24-bit RGB colour space. It also supports animations and whenever you see a logo or other sharp edged line art then you are probably dealing with the GIF format. It uses the lossless data compression technique which reduces the file size without any impact on the quality.
The GIF file format was invented by Compuserve for their online service, but they made the specifications publicly available. GIFs are able to hold multiple bitmaps of up to 256 colors each, using LZW (Lempel Zev Welch - a simple form of file compression that removes inefficiencies in the data storage without losing data or distorting the image) compressed raster data to minimize file sizes. The idea is to lessen the amount of colours in a GIF image to the minimum number necessary and to therefore remove stray colors that are not required to represent the image. A GIF graphic is unable to have more than 256 colors but it can have fewer colors, down to the minimum of two (black and white). Images with fewer colors will compress more efficiently under LZW compression.
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