## Shift Operators in C++ (<< and >>) –

**Left Shift Operator in C++-**

**Right Shift Operator in C++ –**

### How do we apply shifting on unsigned and signed numbers ?

#### Applying shifting on unsigned/positive numbers –

(x<<2) Left Shift Operator Workingx = 0 0 0 1 1 1 1 1 (31 in decimal) x<<1 = 0 0 1 1 1 1 1 0 x<<2 = 0 1 1 1 1 1 0 0

(x>>2)Right Shift Operator Workingx = 0 0 0 1 1 1 1 1 (31 in decimal) x>>1 = 0 0 0 0 1 1 1 1 x>>2 = 0 0 0 0 0 1 1 1

#### Applying shifting on signed numbers –

if the operand is a signed value, then arithmetic shift will be used.

if **x** is negative and the sign bit is 1, so 1’s are shifted from the most significant end. If **x** is non-negative, 0’s are shifted from the most significant end. This is called an *arithmetic right shift* since the sign bit is shifted in.

Negative numbers are represented by 2’s complement. To apply 2’s complement to a decimal number –

- convert decimal number into Binary form.
- take 1’s complement of the binary form i.e. (invert the bits).
- Add Binary 1 to 1’s complement, and the result coming out will be 2’s complement.

An example of shifting on signed numbers are –

Let z = -20 (minus 20)

**2’s Complement and Left Shift – **

0 0 0 1 0 1 0 0 (20 in binary) 1's complement of 20 = 1 1 1 0 1 0 1 1 (invert bits) Adding 1 to 1's complement =+ 0 0 0 0 0 0 0 1 -------------------2's complement of z= 1 1 1 0 1 1 0 0 (-20 in binary)Left shift (<<)= 1 1 0 1 1 0 0 0converting left shift result into decimal by applying 2's complement again -2's complement of left shift result = 0 0 1 0 1 0 0 0 = 40 and adding minus sign =-40 (Answer)

**Right Shift – **

0 0 0 1 0 1 0 0 (20 in binary) 2's complement of z = 1 1 1 0 1 1 0 0 (-20 in binary) Right shift (>>) = 1 1 1 1 0 1 1 0converting arithmetic right shift result into decimal by applying 2's complement again -2's complement of right shift result = 0 0 0 0 1 0 1 0 = 10 and adding minus sign =-10 (Answer)

**Example of C++ program for Shift Operators –**

#include <iostream.h> int main() { int a = 8; int b = -8; int c = 0; c = a >> 1; cout<<"Right shift of a by 1 = "<< c <<endl ; c= b >>1; cout<<"Right Shift of b by 1 = "<< c <<endl; c= b << 1; cout<<"Left Shift of a = "<< c <<endl; c = a << 1; cout<<"Left shift of b = "<< c <<endl;return 0; }

**Output – **

Right shift of a by 1 = 4 Right Shift of b by 1 = -4 Left Shift of a = -16 Left shift of b = 16

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