# Floating Point Comparisons in Matlab

A common problem in Matlab and every other programming language that uses floating point numbers is that calculations involving floats often do not yield the expected answers because of rounding, which can have undesirable effects on control statements. The immediate question is how to handle these rounding errors so that intuitively correct statements are recognized as true by a program. We would like to accomplish this while still retaining as much relevant information in the numbers as possible, thereby allowing the detection of minute differences that are not artifacts of rounding. In this post, some common errors in floating point comparisons will be discussed, as well as methods of handling these errors.

# Conversion of Floating Point Numbers from Binary to Decimal

After introducing floating point numbers and sharing a function to convert a floating point number to its binary representation in the first two posts of this series, I would like to provide a function that converts a binary string to a floating point number. In addition. I will convert between different types of binary representations and discuss their merits.

# Conversion of Floating Point Numbers in Matlab

In the last post on floating point numbers, I presented a brief overview of floating point numbers, introduced several Matlab functions that provide information about floats (realmin, realmax, and eps), and explored the workings of eps. In this post, I would like to introduce a function that I wrote in Matlab to convert a floating point number to its binary representation and use that function to explain the floating-point representations of ten different numbers.

# Floating Point Numbers in Matlab

Floating point numbers are utilized in most calculations performed in Matlab and other programming languages. Often misunderstood, floating-point arithmetic can cause many confounding problems in addition, subtraction, multiplication, division, comparison, and other types of calculations. In this series of posts, I would like to describe the basics of floating point numbers that conform to  IEEE Standard 754 , introduce several Matlab functions that provide information about floating point numbers, provide a pair of functions that convert between the decimal and binary floating point representations, present some examples of how to view floating point numbers in different formats, and demonstrate how to handle some common problems with their arithmetic. In this post, I will give a brief overview of floating point numbers, introduce several Matlab functions that handle floats, and delve into detail of one of these functions named eps.