The decimal representation of a number is a base-10 number system having only ten states 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example, 4, 10, 16, etc.
The Binary representation of a number is a base-2 number system having only two states 0 and 1. For example, the binary representation of 4, a base-9 decimal number system is given by 100, 10 as 1010, 16 as 1000, etc.
Left Shift
The left shift means that shift each of the bits is in binary representation toward the left.
Logical Left Shift
For example, when we say left shift 5 or 101 by one position. We will shift each of the bits by one position towards the left. So after shifting the number 5 towards the left by one position, the number obtained is 10 or 1010. Now let us again left shift 10 by two positions. Again, we will shift each of the bits by two positions towards the left. The number obtained is 40 or 101000.
Note: Left shifting a number by certain positions is equivalent to multiplying the number by two raised to the power of the specified positions. That is,
left shift x by n positions <=> x * 2n
Left Shift Operator in Java
Most of the languages provide left shift operators using which we can left shift a number by certain positions and Java is one of them. The syntax of the left-shift operator in Java is given below,
Syntax:
x << n Here, x: an integer n: a non-negative integer
Return type: An integer after shifting x by n positions toward left
Exception: When n is negative the output is undefined
Below is the program to illustrate how we can use the left shift operator in Java.
Example 1:
Java
// Java program to illustrate the// working of left shift operatorimport java.io.*;class GFG { // Main method public static void main (String[] args) { // Number to be shifted int x = 5; // Number of positions int n = 1; // Shifting x by n positions towards left using left shift operator int answer = x << n; // Print the number obtained after shifting x by n positions towards left System.out.println("Left shift " + x + " by " + n + " positions : " + answer); // Number to be shifted x = answer; // Number of positions n = 2; // Shifting x by n positions towards left using left shift operator answer = answer << n; // Print the number obtained after shifting x by n positions towards left System.out.println("Left shift " + x + " by " + n + " positions : " + answer); }} |
Left shift 5 by 1 positions : 10 Left shift 10 by 2 positions : 40
Example 2:
Java
// Java program to illustrate the// working of left shift operatorimport java.io.*;class GFG { // Main method public static void main (String[] args) { // Number to be shifted int x = -2; // Number of positions int n = 1; // Shifting x by n positions towards // left using left shift operator int answer = x << n; // Print the number obtained after shifting x by n positions towards left System.out.println("Left shift " + x + " by " + n + " positions : " + answer); // Number to be shifted x = answer; // Number of positions n = 2; // Shifting x by n positions towards // left using left shift operator answer = answer << n; // Print the number obtained after shifting x by n positions towards left System.out.println("Left shift " + x + " by " + n + " positions : " + answer); }} |
Left shift -2 by 1 positions : -4 Left shift -4 by 2 positions : -16
Time complexity: O(1)
Space complexity: O(1)
Note: For arithmetic left shift, since filling the right-most vacant bits with 0s will not affect the sign of the number, the vacant bits will always be filled with 0s, and the sign bit is not considered. Thus, it behaves in a way identical to the logical (unsigned) left shift. So there is no need for a separate unsigned left sift operator.
