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In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation. Given two positive numbers a and n , a modulo n (often abbreviated as a mod n ) is the remainder of the Euclidean division of a by n , where a is the dividend and n is the divisor .
The logical operator XOR sums 2 bits, modulo 2. The use of long division to turn a fraction into a repeating decimal in any base b is equivalent to modular multiplication of b modulo the denominator. For example, for decimal, b = 10.
Implements the mathematical modulo operator. The returned result is always of the same sign as the modulus or nul, and its absolute value is lower than the absolute value of the modulus . However, this template returns 0 if the modulus is nul (this template should never return a division by zero error).
Implements the mathematical modulo operator. The returned result is always of the same sign as the modulus or nul, and its absolute value is lower than the absolute value of the modulus . However, this template returns 0 if the modulus is nul (this template should never return a division by zero error).
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b e mod m. From the definition of division, it follows that 0 ≤ c < m. For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8.
Currently the table only does integer modulo operators. (In some languages the floating-point modulo operator is the same as the integer modulo operator; whereas in other languages it is different.) For example, in C, the fmod() function is used to perform floating-point modulo (the % operator won't work); but it is not listed in the table.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.