# The main features of modular arithmetic and its importance

Continuous probability distributions[ edit ] Comparison of two log-normal distributions with equal mean but different skewnessresulting in different medians and modes. If a numerical property, and any sample of data from it, could take on any value from a continuous range, instead of, for example, just integers, then the probability of a number falling into some range of possible values can be described by integrating a continuous probability distribution across this range, even when the naive probability for a sample number taking one certain value from infinitely many is zero. The analog of a weighted average in this context, in which there are an infinite number of possibilities for the precise value of the variable in each range, is called the mean of the probability distribution. Definition - What does Modular Programming mean? Modular programming is the process of subdividing a computer program into separate sub-programs. A module is a separate software component.

It can often be used in a variety of applications and functions with other components of the system. Similar functions are grouped in the same unit of programming code and separate functions are developed as separate units of code so that the code can be reused by other applications.

Object-oriented programming OOP is compatible with the modular programming concept to a large extent. Modular programming enables multiple programmers to divide up the work and debug pieces of the program independently.

Techopedia explains Modular Programming Modules in modular programming enforce logical boundaries between components and improve maintainability. They are incorporated through interfaces.

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They are designed in such a way as to minimize dependencies between different modules. Teams can develop modules separately and do not require knowledge of all modules in the system. Each and every modular application has a version number associated with it. This provides developers flexibility in module maintenance. If any changes have to be applied to a module, only the affected subroutines have to be changed. This makes the program easier to read and understand. Modular programming has a main module and many auxiliary modules.

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The main module is compiled as an executable EXEwhich calls the auxiliary module functions. Auxiliary modules exist as separate executable files, which load when the main EXE runs. Function names across modules should be unique for easy access if functions used by the main module must be exported. The benefits of using modular programming include: Less code has to be written. A single procedure can be developed for reuse, eliminating the need to retype the code many times.

Programs can be designed more easily because a small team deals with only a small part of the entire code. Modular programming allows many programmers to collaborate on the same application.

The code is stored across multiple files. Code is short, simple and easy to understand. Errors can easily be identified, as they are localized to a subroutine or function. The same code can be used in many applications. The scoping of variables can easily be controlled.In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in Read and learn for free about the following article: Modular multiplication If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *initiativeblog.com and *initiativeblog.com are unblocked. The best way to introduce modular arithmetic is to think of the face of a clock.

The numbers go from \$1\$ to \$12\$, but when you get to "\$13\$ o'clock", it actually becomes \$1\$ o'clock again (think of how the \$24\$ hour clock numbering works). MODULAR ARITHMETIC KEITH CONRAD 1. Introduction We will de ne the notion of congruent integers (with respect to a modulus) and develop some basic ideas of modular arithmetic.

Modular arithmetic is a system of arithmetic for integers, which considers the remainder. In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity (this given quantity is known as the modulus) to leave a remainder.

## What is modular arithmetic? (article) | Khan Academy

The importance of mathematics The everyday use of arithmetic and the display of information by means of graphs, are an everyday commonplace. These are the elementary aspects of mathematics. Advanced mathematics is widely used, but often in an unseen and unadvertised way.

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