# Mod (modulo or redundancy)

Source: Internet
Author: User

1. Residual: The remainder after the division is divided, for example:

MOD 4 = 2;   -17 MOD 4 =-1;    -3 MOD 4 =-3;    4 MOD (-3) = 1; -4 MOD 3 =-1;

If a mod B is an XOR, then the resulting symbol is the same as a; Of course, a mod B is equivalent to a-(a DIV b) *b operation. For example:

MOD 4 =-(4 DIV.) * 4 = 13-12 = 1

(XOR rule: A% B = C, the value of C is: | a| % | b| results, let the result be the same as a, and then add to B. For example: |-15| % |4| = 3,

Then-3 + 4 = 1, if it is 15 (-4), then the result is 3 + (-4) =-1, note that must be two number of different numbers is the rule, the same number is the same as the general algorithm)

2. Modulo: "A MOD B" can not be negative, and its operation rules are as follows:

1) When a > B, continuously subtract b from a, until a non-negative number less than B is present.

Example: 8 MOD 3 = 2

2) When a < B, and a > 0 o'clock, the result is a.

Example: 3 MOD 8 = 3

3) When a < B, and a < 0 o'clock, B is continuously added to a, until the result is a non-negative number less than B.

Example:-3 mod 4 = 1,-4 mod 3 = 2

Note: When A and B are all positive, the results are the same, whether it is "seeking redundancy" or "seeking for a model". such as: MOD 6 = 4, only when a < 0 o'clock, the results of the two operations

Different.

For example: N is four digits 7341, you can use the following method to isolate its, ten, hundred, thousands.

7431 MOD 10 = 1 (single digit)

(7431 MOD 100) DIV 10 = 4 (10-digit)

(7431 MOD 1000) DIV 100 = 3 (hundred numbers)

7431 DIV 1000 = 7 (Thousand numbers)

Also, using a MOD B, you can tell if a can be divisible by B. When a MOD b = 0 o'clock, a can be divisible by B.

Note: A and B must be integers. For example: 50.0 MOD 20.0 is not possible.

Note: The mold can be regarded as positioning, such as%10 positioning to bits,%100 positioning to the hundred. The div can be seen as the number of bits to be determined.

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