<Li> Tremor, Toast and MAD are software libraries which decode the Ogg Vorbis, GSM Full Rate and MP3 audio formats respectively . These codecs use fixed - point arithmetic because many audio decoding hardware devices do not have an FPU (partly to save money, but primarily to save power - integer units are much smaller in silicon area than an FPU) and audio decoding requires performance to the extent a software implementation of floating - point on low - speed devices would not produce output in real time . </Li> <Li> All 3D graphics engines on Sony's original PlayStation, Sega's Saturn, Nintendo's Game Boy Advance (only 2D), Nintendo DS (2D and 3D), Nintendo Gamecube and GP2X Wiz video game systems use fixed - point arithmetic for the same reason as Tremor and Toast: to gain throughput on an architecture without an FPU (e.g. the PlayStation included hardware support for 4.12 bit values in its transformation coprocessor). </Li> <Li> The OpenGL ES 1. x specification includes a fixed point profile, as it is an API aimed for embedded systems, which do not always have an FPU . </Li> <Li> TeX font metric files use 32 - bit signed fixed - point numbers, with 12 bits to the left of the decimal, extensively . </Li>

When does an overflow occur in fixed point representation