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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.
In this case, s is called the least absolute remainder. [3] As with the quotient and remainder, k and s are uniquely determined, except in the case where d = 2n and s = ± n. For this exception, we have: a = k⋅d + n = (k + 1)d − n. A unique remainder can be obtained in this case by some convention—such as always taking the positive value ...
In the part of the basic Sarwate algorithm where the previous CRC value is shifted by the size of the table lookup, the previous CRC value is shifted away entirely (what remains is all zero), so the XOR can be eliminated from the critical path. The resultant slice-by-n inner loop consists of: XOR the current CRC with the next n bytes of the ...
which is the shorthand way of writing the statement that m divides (evenly) the quantity ax − 1, or, put another way, the remainder after dividing ax by the integer m is 1. If a does have an inverse modulo m, then there are an infinite number of solutions of this congruence, which form a congruence class with respect to this modulus.
The long division may begin with a non-zero remainder. The remainder is generally computed using an -bit shift register holding the current remainder, while message bits are added and reduction modulo () is performed. Normal division initializes the shift register to zero, but it may instead be initialized to a non-zero value.
where 0 ≤ r < m is the common remainder. We recover the previous relation ( a − b = k m ) by subtracting these two expressions and setting k = p − q . Because the congruence modulo m is defined by the divisibility by m and because −1 is a unit in the ring of integers, a number is divisible by − m exactly if it is divisible by m .
To calculate the check digit, take the remainder of (53 / 10), which is also known as (53 modulo 10), and if not 0, subtract from 10. Therefore, the check digit value is 7. i.e. (53 / 10) = 5 remainder 3; 10 - 3 = 7. Another example: to calculate the check digit for the following food item "01010101010x". Add the odd number digits: 0+0+0+0+0+0 = 0.
At points of discontinuity, a Fourier series converges to a value that is the average of its limits on the left and the right, unlike the floor, ceiling and fractional part functions: for y fixed and x a multiple of y the Fourier series given converges to y/2, rather than to x mod y = 0. At points of continuity the series converges to the true ...
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