The Floating-point is a method for representing real numbers (i.e., numbers that can have a fractional part) in a way that can support a very wide range of values, from extremely small to extremely large. A floating-point number is represented in a form similar to scientific notation, typically divided into three parts: a sign bit (indicating positive or negative), an exponent, and a mantissa (or significand). The mantissa contains the number's significant digits, while the exponent specifies the position of the "floating" decimal (or binary) point.
The most common standard for this representation is IEEE 754, which defines formats like 32-bit (single-precision) and 64-bit (double-precision). This system is used by virtually all modern CPUs for performing non-integer arithmetic. In the context of programmable power supplies and measurement instruments, floating-point numbers are essential. They are used to represent setpoints (e.g., 12.345 V) and measurement results (e.g., 1.567 A) with high precision and a wide dynamic range. However, it's important to understand their limitation: because they have a finite number of bits for the mantissa, they cannot represent all real numbers with perfect accuracy. This can lead to small rounding errors and precision loss in calculations, which must be considered in high-accuracy applications. For most control and measurement tasks, the precision offered by standard floating-point types is more than sufficient.