Given a number n, write a function that returns true if n is divisible by 9, else false. The most simple way to check for n’s divisibility by 9 is to do n%9.
Another method is to sum the digits of n. If sum of digits is multiple of 9, then n is multiple of 9.
The above methods are not bitwise operators based methods and require use of % and /.
The bitwise operators are generally faster than modulo and division operators. Following is a bitwise operator based method to check divisibility by 9.
0 9 18 27 36 45 54 63 72 81 90 99
How does this work?
n/9 can be written in terms of n/8 using the following simple formula.
n/9 = n/8 - n/72
Since we need to use bitwise operators, we get the value of floor(n/8) using n>>3 and get value of n%8 using n&7. We need to write above expression in terms of floor(n/8) and n%8.
n/8 is equal to “floor(n/8) + (n%8)/8”. Let us write the above expression in terms of floor(n/8) and n%8
n/9 = floor(n/8) + (n%8)/8 - [floor(n/8) + (n%8)/8]/9 n/9 = floor(n/8) - [floor(n/8) - 9(n%8)/8 + (n%8)/8]/9 n/9 = floor(n/8) - [floor(n/8) - n%8]/9
From above equation, n is a multiple of 9 only if the expression floor(n/8) – [floor(n/8) – n%8]/9 is an integer. This expression can only be an integer if the sub-expression [floor(n/8) – n%8]/9 is an integer. The subexpression can only be an integer if [floor(n/8) – n%8] is a multiple of 9. So the problem reduces to a smaller value which can be written in terms of bitwise operators.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- Check if a Number is Odd or Even using Bitwise Operators
- Check if a number is divisible by 17 using bitwise operators
- Check if a number is divisible by 8 using bitwise operators
- Check if a number is positive, negative or zero using bit operators
- Bitwise Operators in C/C++
- Check whether bitwise AND of a number with any subset of an array is zero or not
- What are the differences between bitwise and logical AND operators in C/C++?
- Bitwise right shift operators in Java
- Check whether a very large number of the given form is a multiple of 3.
- Toggle case of a string using Bitwise Operators
- Write an Efficient Method to Check if a Number is Multiple of 3
- Russian Peasant (Multiply two numbers using bitwise operators)
- Case conversion (Lower to Upper and Vice Versa) of a string using BitWise operators in C/C++
- Total pairs in an array such that the bitwise AND, bitwise OR and bitwise XOR of LSB is 1
- Check whether bitwise AND of N numbers is Even or Odd
- Check whether bitwise OR of N numbers is Even or Odd
- Check if bitwise AND of any subset is power of two
- Check if n is divisible by power of 2 without using arithmetic operators
- Check if two numbers are equal without using comparison operators
- Check if two numbers are equal without using arithmetic and comparison operators
Improved By : nitin mittal