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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}
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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.
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.
