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In ordinary arithmetic, the resulting value will be from an infinite set of values but in case modular arithmetic, resulting value will be from a finite set of values.
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e.g. in ordinary arithmetic, the sum of two integers, the result will be an integer in the range {..., -3, -2, -1, 0, 1, 2, 3, ...}
for modular arithmetic, the sum of two integers
like (a+b)mod n will be in the range {0, 1, 2, ... n-1}
What else can I help you with?
What is equivalent to 32 96?
32 is equivalent to 96 when considering both numbers in the context of modular arithmetic. In modular arithmetic, two numbers are considered equivalent if they have the same remainder when divided by a specific modulus. In this case, if we consider the numbers 32 and 96 modulo 64 (32 mod 64 = 32 and 96 mod 64 = 32), they are equivalent.
Difference between servlet engines and servlet chaining?
Servlet engines are software components that manage the execution of servlets, handling requests and responses, and providing an environment for servlets to run within a web server. In contrast, servlet chaining refers to the practice of invoking multiple servlets in a sequence, where the output of one servlet can be passed as input to another, allowing for modular and reusable components in web applications. Essentially, servlet engines provide the infrastructure, while servlet chaining is a design technique for enhancing functionality within that infrastructure.
Why does 1 plus 1 equals 0 in binary?
1 + 1 = 0 in binary. Why does this happen?Note: Adding binary numbers is related to modulo 2 arithmetic.Let's review mod and modular arithmetic with addition.modulus 2 is the mathematical term that is the remainder from the quotient of any term and 2. For instance, if we have 3 mod 2, then we have 3 / 2 = 1 + ½. The remainder is 1. So 3 ≡ 1 mod 2.What if we want to add moduli?The general form is a mod n + b mod n ≡ (a + b) mod n.Now, for the given problem, 1 mod 2 + 1 mod 2 ≡ 2 mod 2. Then, 2 mod 2 ≡ 0 mod 2.Therefore, 1 + 1 = 0 in binary.
What is the last digit of 333 to the power of 444?
To find the last digit of a number raised to a power, we can use the concept of modular arithmetic. The last digit of 333 to the power of 444 can be determined by finding the remainder when 333 is divided by 10, which is 3. Since the last digit of 333 is 3, we need to find the remainder of 444 divided by 4, which is 0. Therefore, the last digit of 333 to the power of 444 is the same as the last digit of 3 to the power of 4, which is 1.
What is non modular bricks?
Difference between modular and non-modular bricks
What is the difference between modular arithmetic and ordinary arthmetic?
given any positive integer n and any integer a , if we divide a by n, we get an integer quotient q and an integer remainder r that obey the following relationship where [x] is the largest integer less than or equal to x
What is difference between modular or non modular router?
additional ports can be added in modular routers.
Which mathematician discovered modular arithmetic?
According to Wikipedia, Carl Friedrich Gauss invented it. Quote Wikipedia,"Modular arithmetic was introduced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801."
What are some differences between modular arithmetic and real numbers?
Modular arithmetic operates within a finite set of integers, where numbers wrap around upon reaching a specified modulus, effectively creating a cyclical structure. In contrast, real numbers include all rational and irrational values, extending infinitely in both positive and negative directions without any modulus constraints. While modular arithmetic focuses on equivalence classes of numbers under a specific modulus, real numbers provide a continuous scale for measurement and calculation. Additionally, operations in modular arithmetic can yield different results than those in the real number system due to the wrap-around effect inherent in its structure.
In modular arithmetic must the modular always be greater than the remainder?
Yes, because that is how remainder is defined. If the remainder was bigger, you would subtract one (or more) modular values until the remainder became smaller than the modulus.
How clock is related in math?
A clock is a practical application of concepts in mathematics, particularly in understanding angles, time measurement, and modular arithmetic. The face of a clock is divided into 12 hours, creating a circular representation of time where each hour represents a 30-degree segment (360 degrees divided by 12). Additionally, when calculating elapsed time or determining the time difference, modular arithmetic is used, often expressed in terms of modulo 12. This relationship highlights the connection between geometry, number theory, and everyday timekeeping.
What is the difference between mobile and modular homes?
On a basic level, the difference between mobile and modular homes is quality. Mobile homes have not been built since 1976 because of stricter standards enacted by the US Department of Housing and Development (HUD). Modular homes are movable, but like site-based homes, have strict codes and standards to meet before being made for sale to a prospective home owner.
When does four plus four equal 9?
In standard arithmetic, four plus four equals 8. However, in certain mathematical systems, such as modular arithmetic, where numbers "wrap around" after reaching a certain value, four plus four can equal 9. This is because in modular arithmetic, numbers are considered congruent if they have the same remainder when divided by a specific number, known as the modulus.
How can you use 4 9's to make 23?
It is impossible to make 23 from four 9's unless modular arithmetic is involved, in this case in mod 40, 57, 58, 59, 76, 697, 6538. I personally can't see any other way to obtain 23 other than modular arithmetic.
What is the difference between modular and pre-fab homes?
They are essentially equivelent in common usage, but technically, a pre-fab home has its components all built offsite and assembled at the building site while modular homes generally don't.
What are finite sets?
They are sets with a finite number of elements. For example the days of the week, or the 12 months of the year. Modular arithmetic is based on finite sets.
