Bit manipulation is a technique that involves directly manipulating the individual bits of a number. It's often used to optimize algorithms and solve problems efficiently.

BITWISE OPERATORS

Observations of XOR :

• a ^ 1 = ā (compliment of a)

• a ^ 0 = a

• a ^ a = 0

Right Shift Operator [\>>] -> shifts bits to the right , filling the vacant positions with zero(0).

General Point :

a >> b = a / (2^b)

Left Shift Operator [<<] -> Shifts bits to the left , filling the vacant positions with zero again.

General Point :

num << 1 == 2(num)

a << b = a (2^b)

Number System Conversion

The binary number system is a base-2 numeral system that uses only two digits, 0 and 1. This system is fundamental to modern computers and digital electronics because it's easy to represent with electrical signals (on/off, high/low voltage).

• conversation steps :

  • 1. Decimal to Base B

       keep Diving by base , take the remainder ,Write in opposite

       2. Base B to decimal

          multiply and add the power of base with digits

• 

 int n =10;
        System.out.println(Integer.toBinaryString(n));

Output :
1010

Negative of a Number

1. Take a compliment of that number

2. Add 1 to it

3. 

Most Significant Bit - Tells whether the number is +VE or -VE.

• 0 -> Negative

• 1-> Positive

  Least Significant Bit - tells whether the number is ODD or EVEN.

• 0 -> EVEN

• 1 -> ODD

  Range of Numbers

Range Formula :