Search results
Results from the WOW.Com Content Network
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.
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.
Code fragment 6: Cores of table based division Using a 256-entry table is usually most convenient, but other sizes can be used. In small microcontrollers, using a 16-entry table to process four bits at a time gives a useful speed improvement while keeping the table small.
Given an integer a and a non-zero integer d, it can be shown that there exist unique integers q and r, such that a = qd + r and 0 ≤ r < | d |. The number q is called the quotient, while r is called the remainder. (For a proof of this result, see Euclidean division. For algorithms describing how to calculate the remainder, see Division algorithm.)
For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0. Although typically performed with a and n both being integers, many computing systems now allow other types of numeric operands.
Based on an algorithm used widely by programmers coding in assembly for minimizing the number of tests and branches during a copy, Duff's device appears out of place when implemented in C. The device is valid C by virtue of two attributes in C: Relaxed specification of the switch statement in the language's definition.
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
When all digits have been processed and no remainder is left, the process is complete. An example is shown below, representing the division of 500 by 4 (with a result of 125). 1 2 5 (Explanations) 4)500 4 ( 4 × 1 = 4) 1 0 ( 5 - 4 = 1) 8 ( 4 × 2 = 8) 2 0 (10 - 8 = 2) 20 ( 4 × 5 = 20) 0 (20 - 20 = 0) An example of long division performed ...