You are given an positive integer n as dividend and another number m (form of 2^k), you have to find quotient and remainder without performing actual division.
Input : n = 43, m = 8 Output : Quotient = 5, Remainder = 3 Input : n = 58, m = 16 Output : Quotient = 3, Remainder = 10
In this we are using bitwise representation of a number for understanding the role of division of any number by divisor of form 2^k. All numbers which are power of two includes only 1 set bits in their representation and we will use this property.
For finding remainder we will take logical AND of the dividend (n) and divisor minus 1 (m-1), this will give only the set bits of dividend right to the set bit of divisor which is our actual remainder in that case.
Further, the left part of the dividend (from the position of set bit in divisor) would be considered for quotient. So, from dividend (n) removing all bits right from the position of set bit of divisor will result into quotient, and right shifting the dividend log2(m) times will do this job for finding the quotient.
- Remainder = n & (m-1)
- Quotient = (n >> log2(m) )
Note : Log2(m) will give the number of bits present in the binary representation of m.
Remainder = 3 Quotient = 5
- Count of divisors having more set bits than quotient on dividing N
- Check if given number is a power of d where d is a power of 2
- Program to find remainder when large number is divided by r
- Program to find remainder when large number is divided by 11
- Fibonacci Power
- Multiplication with a power of 2
- Number of pairs whose sum is a power of 2
- Find whether a given integer is a power of 3 or not
- Program to find whether a no is power of two
- Check if a number is power of 8 or not
- Find whether a given number is a power of 4 or not
- Smallest power of 2 greater than or equal to n
- Highest power of 2 less than or equal to given number
- Minimum absolute difference between N and a power of 2
- Check if bitwise AND of any subset is power of two
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.