## Introduction To Bitwise Operations

Bitwise operators are used to change individual bits in an operand.
The main use of bitwise operations are to perform calculations at a more optimized level as these operations are directly supported by the processor.
• & (bitwise AND) Takes two numbers as operands and does AND on every bit of two numbers. The result of AND is 1 only if both bits are 1.
eg: 1010 & 0010 = 0010
• | (bitwise OR) Takes two numbers as operands and does OR on every bit of two numbers. The result of OR is 1 any of the two bits is 1.
eg: 1001 | 0010 = 1011
• ^ (bitwise XOR) Takes two numbers as operands and does XOR on every bit of two numbers. The result of XOR is 1 if the two bits are different.
eg: 0110 ^ 1000 = 1110
• << (left shift) Takes two numbers, left shifts the bits of the first operand, the second operand decides the number of places to shift.
eg: 0101 << 1 = 1010
• >> (right shift) Takes two numbers, right shifts the bits of the first operand, the second operand decides the number of places to shift.
eg: 0010 >> 1 = 0001
• ~ (bitwise NOT) Flips all the bits.
eg : ~1001 = 0110
*Note : When it comes to shifting bits there are mainly 3 types : Arithmetic Shift, Logical Shift & Circular Shift.
These variations are there to handle the cases where the bits at the edge of the bit field are about to be shifted out of the bit field.

### Let's Look At A C# Example

``````using System;
namespace BitshiftProductions
{
public class Program
{
public static void Main(string[] args)
{
int x = 14; // 00001110
int y = 28; // 00011100

Console.WriteLine("x = " + x + " in binary : " + Convert.ToString(x, 2));
Console.WriteLine("y = " + y + " in binary : " + Convert.ToString(y, 2));

int k = x|y;
Console.WriteLine("X OR Y = " + k + " in binary : " + Convert.ToString(k, 2));

k = x&y;
Console.WriteLine("X AND Y = " + k + " in binary : " + Convert.ToString(k, 2));

k = x^y;
Console.WriteLine("X XOR Y = " + k + " in binary : " + Convert.ToString(k, 2));

k = x<<2;
Console.WriteLine("Left Shifted x(14) by 2 places = " + k + " in binary : " + Convert.ToString(k,2));
k = x>>2;
Console.WriteLine("Right Shifted x(14) by 2 places = " + k + " in binary : "+ Convert.ToString(k,2));

k = ~x;
Console.WriteLine("NOT x = " + k + " in binary : "+ Convert.ToString(k,2));
}
}
}
``````
```x = 14 in binary : 1110
y = 28 in binary : 11100
X OR Y = 30 in binary : 11110
X AND Y = 12 in binary : 1100
X XOR Y = 18 in binary : 10010
Left Shifted x(14) by 2 places = 56 in binary : 111000
Right Shifted x(14) by 2 places = 3 in binary : 11
NOT x = -15 in binary : 11111111111111111111111111110001
```
*Note : Leading zeros are not printed with Convert.ToString(object, base) method. All these are 32 bit numbers so the actual bit string would have 32 spaces.

### Common Use Cases Of Bitwise Operations

``````using System;
namespace BitshiftProductions
{
public class Program
{
public static void Main(string[] args)
{
int num = 8;
// 1. Dividing By 2
int k = num >> 1;
Console.WriteLine("Num = 8, Divide By 2 = " + k);
// 2. Multiply By 2
k = num << 1;
Console.WriteLine("Num = 8, Multiply By 2 = " + k);
// 3. Checking If A Number Is Odd Or Even
k = num & 1;//(num & 1) would be non-zero only if x is odd, otherwise the value would be zero.
Console.WriteLine("Is num Odd Or Even : " + ((k != 0)?"Odd":"Even"));
// 4. Check If 2 integers Have Opposite Signs
Console.WriteLine("Do -100 & 50 have same sign ? : " + ((-100 ^ 50) >= 0));
// 5. Find log base 2 of 32 bit integer
int res = 0;
int temp = num;
while (temp > 1)
{
temp = temp >> 1;
res++;
}
Console.WriteLine("Log Base 2 of NUM(8) : " + res);
}
}
}
``````
```Num = 8, Divide By 2 = 4
Num = 8, Multiply By 2 = 16
Is num Odd Or Even : Even
Do -100 & 50 have same sign ? : False
Log Base 2 of NUM(8) : 3
```
I hope to have introduced you to the world of bit manipulation. All the things you learnt today can be easily implemented into your existing projects.
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