In this post, we will teach you about floating point numbers, why they are called that, and how they are represented. We will also explore key concepts like the mantissa and discuss how these numbers are used in computing.
What is floating point called?
A floating point is a method for representing real numbers in computing that includes a fractional part. It is named “floating” because the decimal point can move (“float”) depending on the value of the number, allowing for the representation of a wide range of magnitudes. Floating point numbers are an essential part of modern computing, particularly in fields requiring high precision, such as scientific and financial computations.
Why is it called floating point?
The term “floating point” comes from the flexibility of the decimal point in the number’s representation. Unlike fixed-point numbers, where the decimal point is set in a specific position, floating point numbers allow the decimal to “float” based on the exponent. This floating allows the system to represent very large and very small numbers with a high degree of precision. The floating nature makes it possible to handle calculations across a wide range of magnitudes, from minuscule fractions to huge values.
What is the function of a microcontroller on an Arduino board?
What is a floating point number?
A floating point number is a number that can represent both integers and real numbers with fractional parts. These numbers are composed of three main parts: a sign bit (indicating whether the number is positive or negative), an exponent (which adjusts the magnitude of the number), and a mantissa (which holds the significant digits of the number). This structure allows floating point numbers to handle very small or very large values efficiently but introduces the possibility of rounding errors because not all decimal values can be precisely represented in binary form.
What is floating point mantissa?
The mantissa, also known as the significand, is the part of a floating point number that contains its significant digits. In a floating point representation, the mantissa is combined with the exponent to determine the overall value of the number. The larger the number of bits allocated to the mantissa, the greater the precision of the floating point number. However, increasing the mantissa size comes at the cost of using more memory, which can be a disadvantage in memory-constrained environments.
How is a floating point number represented?
A floating point number is represented in binary using a specific format, typically following the IEEE 754 standard. The number is divided into three parts: the sign bit, the exponent, and the mantissa. The sign bit indicates whether the number is positive or negative. The exponent determines how far the decimal point should “float” from its base position. Finally, the mantissa holds the significant digits, normalized in such a way that the first digit is always non-zero, ensuring efficient use of space. This representation enables a balance between range and precision, but it can also introduce challenges, such as rounding errors in certain operations.
We hope this explanation helped you understand the fundamental aspects of floating point numbers and how they work. Gaining a clear understanding of this concept is critical when working with numerical data in computing.
