It is recommended to refer Interesting facts about Bitwise Operators as a prerequisite.
1. How to set a bit in the number ‘num’ :
If we want to set a bit at nth position in number ‘num’ ,it can be done using ‘OR’ operator( | ).
- First we left shift ‘1’ to n position via (1<<n)
- Then, use ‘OR’ operator to set bit at that position.’OR’ operator is used because it will set the bit even if the bit is unset previously in binary representation of number ‘num’.
We have passed the parameter by ‘call by reference’ to make permanent changes in the number.
2. How to unset/clear a bit at n’th position in the number ‘num’ :
Suppose we want to unset a bit at nth position in number ‘num’ then we have to do this with the help of ‘AND’ (&) operator.
- First we left shift ‘1’ to n position via (1<<n) than we use bitwise NOT operator ‘~’ to unset this shifted ‘1’.
- Now after clearing this left shifted ‘1’ i.e making it to ‘0’ we will ‘AND'(&) with the number ‘num’ that will unset bit at nth position position.
3. Toggling a bit at nth position :
Toggling means to turn bit ‘on'(1) if it was ‘off'(0) and to turn ‘off'(0) if it was ‘on'(1) previously.We will be using ‘XOR’ operator here which is this ‘^’. The reason behind ‘XOR’ operator is because of its properties.
- Properties of ‘XOR’ operator.
- 1^1 = 0
- 0^0 = 0
- 1^0 = 1
- 0^1 = 1
- If two bits are different then ‘XOR’ operator returns a set bit(1) else it returns an unset bit(0).
4. Checking if bit at nth position is set or unset:
It is quite easily doable using ‘AND’ operator.
- Left shift ‘1’ to given position and then ‘AND'(‘&’).
Observe that we have first left shifted ‘1’ and then used ‘AND’ operator to get bit at that position. So if there is ‘1’ at position ‘pos’ in ‘num’, then after ‘AND’ our variable ‘bit’ will store ‘1’ else if there is ‘0’ at position ‘pos’ in the number ‘num’ than after ‘AND’ our variable bit will store ‘0’.
Some more quick hacks:
- Inverting every bit of a number/1’s complement:
If we want to invert every bit of a number i.e change bit ‘0’ to ‘1’ and bit ‘1’ to ‘0’.We can do this with the help of ‘~’ operator. For example : if number is num=00101100 (binary representation) so ‘~num’ will be ‘11010011’.
This is also the ‘1s complement of number’.
- Two’s complement of the number: 2’s complement of a number is 1’s complement + 1.
So formally we can have 2’s complement by finding 1s complement and adding 1 to the result i.e (~num+1) or what else we can do is using ‘-‘ operator.
This is two's complement -4 This is also two's complement -4
- Stripping off the lowest set bit :
In many situations we want to strip off the lowest set bit for example in Binary Indexed tree data structure, counting number of set bit in a number.
We do something like this:
X = X & (X-1)
But how does it even work ?
Let us see this by taking an example, let X = 1100.
(X-1) inverts all the bits till it encounter lowest set ‘1’ and it also invert that lowest set ‘1’.
X-1 becomes 1011. After ‘ANDing’ X with X-1 we get lowest set bit stripped.
- Getting lowest set bit of a number:
This is done by using expression ‘X &(-X)’Let us see this by taking an example:Let X = 00101100. So ~X(1’s complement) will be ‘11010011’ and 2’s complement will be (~X+1 or -X) i.e ‘11010100’.So if we ‘AND’ original number ‘X’ with its two’s complement which is ‘-X’, we get lowest set bit.
00101100 & 11010100 ----------- 00000100
Refer BitWise Operators Articles for more articles on Bit Hacks.
This article is contributed by Pankaj Mishra. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
- Tips and Tricks for Competitive Programmers | Set 2 (Language to be used for Competitive Programming)
- How can competitive programming help you get a job?
- A Better Way To Approach Competitive Programming
- Fast I/O for Competitive Programming
- Which C++ libraries are useful for competitive programming?
- Python in Competitive Programming
- How to begin with Competitive Programming?
- C++ tricks for competitive programming (for C++ 11)
- Bit Tricks for Competitive Programming
- What is Competitive Programming and How to Prepare for It?
- How to become a master in competitive programming?
- Must do Math for Competitive Programming
- What Are The Best Resources For Competitive Programming?
- Which Java libraries are useful for competitive programming?
- Competitive Programming: Conquering a given problem
- Which Python Modules are useful for competitive programming?
- Importance of Testing In Competitive Programming
- Setting up a C++ Competitive Programming Environment
- Interactive Problems in Competitive Programming
- Logarithm tricks for Competitive Programming
Improved By : jit_t