  There is a growing interest in the use of reduced-precision arithmetic,
exacerbated by the recent interest in artificial intelligence, especially with
deep learning. Most architectures already provide reduced-precision
capabilities (e.g., 8-bit integer, 16-bit floating point). In the context of
FPGAs, any number format and bit-width can even be considered.In computer
arithmetic, the representation of real numbers is a major issue. Fixed-point
(FxP) and floating-point (FlP) are the main options to represent reals, both
with their advantages and drawbacks. This chapter presents both FxP and FlP
number representations, and draws a fair a comparison between their cost,
performance and energy, as well as their impact on accuracy during
computations.It is shown that the choice between FxP and FlP is not obvious and
strongly depends on the application considered. In some cases, low-precision
floating-point arithmetic can be the most effective and provides some benefits
over the classical fixed-point choice for energy-constrained applications.
