Mantissaa

Mantissaa is a term used in computing and mathematics to refer to the fractional part of a floating-point number. In the context of a floating-point representation, a number is typically expressed in the form of a * mantissaa * 10^exponent, where the mantissaa represents the significant digits of the number. For example, in the number 3.14159, the mantissaa is 314159 and the exponent is -5.

The mantissaa is crucial in the representation of floating-point numbers because it determines the precision of the number. The number of digits in the mantissaa affects the accuracy with which the number can be represented. In binary floating-point systems, which are commonly used in computers, the mantissaa is often normalized to have a leading digit of 1, which is not explicitly stored to save space.

The term "mantissaa" is derived from the Latin word "mantissa," which means "appendix" or "addition." This reflects the historical use of the term in the context of logarithms, where the mantissaa was the part of the logarithm that needed to be added to the characteristic to obtain the full logarithm of a number.

In modern computing, the mantissaa is a fundamental component of floating-point arithmetic, which is used to perform calculations involving real numbers. The IEEE 754 standard defines the format for floating-point arithmetic, including the representation of the mantissaa, exponent, and sign bit. The standard specifies different precisions, such as single precision (32 bits) and double precision (64 bits), each with its own format for the mantissaa and exponent.