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Definition. The Modulus is the remainder of the euclidean division of one number by another. % is called the modulo operation. For instance, 9 divided by 4 equals 2 but it remains 1. Here, 9 / 4 = 2 and 9 % 4 = 1. In your example: 5 divided by 7 gives 0 but it remains 5 (5 % 7 == 5). Calculation.
Step-1: When you divide a number ω by n then reminder can be either 0, 1, ..., (n - 2) or (n - 1). If remainder is 0 that means ω is divisible by n otherwise not. So, in my DFA there will be a state q r that would be corresponding to a remainder value r, where 0 <= r <= (n - 1), and total number of states in DFA is n.
1 mod 5 = 1, but it can also equal -4. That is, 1/5 yields a remainder 1 from 0 or -4 from 5. (Both factors of 5) Similarly, -1 mod 5 = -1, but it can also equal 4. That is, -1/5 yields a remainder -1 from 0 or 4 from -5. (Both factors of 5) For further reading look into equivalence classes in Mathematics.
Although Java has a remainder operator for int and long types, it has no modulus function or operator. I.e., -12 % 10 = -2 whereas -12 mod 10 = 8. If % operator returns a negative value for n % m, then (n % m) + m will give you n mod m. BigInteger provides functions for both and the specifications for them explain the difference quite well.
0. Modulo Method First need to divide the Dividend by the Divisor: 2 4 = 0.50 Next we take the Whole part of the Quotient (0) and multiply that by the Divisor (4): 0 x 4 = 0. And finally, we take the answer in the second step and subtract it from the Dividend to get the answer to 2 mod 4: 2 - 0 = 2.
28. mod = a % b. This stores the result of a mod b in the variable mod. And you are right, 15 mod 4 is 3, which is exactly what python returns: >>> 15 % 4. 3. a %= b is also valid. edited Jul 28, 2019 at 16:12. wjandrea.
5 % 2 = 1 13 % 5 = 3 With this knowledge we can try to understand your code. Condition count % 6 == 5 means that newline will be written when remainder of division count by 6 is five. How often does that happen? Exactly 6 lines apart (excercise : write numbers 1..30 and underline the ones that satisfy this condition), starting at 6-th line ...
0. Say you want to map from 1 to n not 0 to n-1 eg n=5, range 1 to x, results 0 to 4,0mod5=0 1mod5=1, 2mod5=2... xmod5 results 0 whenever x=5*k. Use ( (x-1)mod5)+1, x must be >0. This will always map (count) in 1 to 5 range, instead 0 to 4. answered Mar 29, 2021 at 20:17.
If: (a+b) mod N = ((a mod N) + (b mod N)) mod N. then: (a - 2*b + 1) mod N = ((a mod N) - (b mod N) - (b mod N) + (1 mod N)) mod N It is simpler with large values of a and b and a small value for N. For example: a=85773, b = 77733340, N=5: which would you rather solve (85773 - 77733340 - 77733340 + 1) mod 5 or
Modulus is just the remainder in division before its used in a decimal quotient. Example: The division of two numbers is often expressed as a decimal number (quotient). But the result of the division of say, 1/3, can also be expressed in whole numbers as "0 with a remainder of 1". But that form of quotient is not very helpful in modern math, so ...