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https://github.com/sk-azraf-sami/bit-manipulation

Bit manipulation is much important in problem solving context. But this topic is so much confusing.So, I created this note as a overview on bit manipulation
https://github.com/sk-azraf-sami/bit-manipulation

bit-manipulation bitmanipulation c contest-programming puzzle

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Bit manipulation is much important in problem solving context. But this topic is so much confusing.So, I created this note as a overview on bit manipulation

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README 

        
# Bit Manipulation in 'C' Programming



## Basic 

Bitwise operators are fundamental operators in computer programming that work on individual bits (0s and 1s) within binary representations of numbers. These operators are commonly used in low-level programming, hardware manipulation, and various other applications. There are several bitwise operators:



1. **Bitwise AND (`&`):** This operator compares each bit position of two integers. If both bits are 1, the result is 1; otherwise, it's 0.



   Example:

   ```

   5 (binary: 0101)

   & 3 (binary: 0011)

   = 1 (binary: 0001)

   ```



2. **Bitwise OR (`|`):** This operator compares each bit position of two integers. If either of the bits is 1, the result is 1; otherwise, it's 0.



   Example:

   ```

   5 (binary: 0101)

   | 3 (binary: 0011)

   = 7 (binary: 0111)

   ```



3. **Bitwise XOR (`^`):** This operator compares each bit position of two integers. If the bits are different (one is 0, the other is 1), the result is 1; otherwise, it's 0.



   Example:

   ```

   5 (binary: 0101)

   ^ 3 (binary: 0011)

   = 6 (binary: 0110)

   ```



4. **Bitwise NOT (`~`):** This operator negates each bit. It flips 0s to 1s and 1s to 0s.



   Example:

   ```

   ~5 (binary: 0101)

   = -6 (binary: 1010)

   ```



5. **Left Shift (`<<`):** This operator shifts the bits of a number to the left by a specified number of positions. It effectively multiplies the number by 2 for each position shifted.



   Example:

   ```

   5 << 2

   = 20

   ```



6. **Right Shift (`>>`):** This operator shifts the bits of a number to the right by a specified number of positions. It effectively divides the number by 2 for each position shifted.



   Example:

   ```

   20 >> 2

   = 5

   ```



Bitwise operators are often used in scenarios such as:



- Manipulating individual bits within a number.

- Efficiently implementing data structures like bitsets and flags.

- Performing optimizations in low-level code.

- Interacting with hardware registers.

- Encoding and decoding data in specific formats.



Understanding bitwise operators is crucial when working on embedded systems, system-level programming, and tasks requiring precise control over data at the bit level.



**Difference between ~ and ! of bitwise operation**



The `~` and `!` operators are both used in bitwise operations, but they serve different purposes and have different behaviors:



1. `~` (Bitwise NOT Operator):

   - `~` is the bitwise NOT operator, also known as the bitwise complement operator.

   - It inverts each bit in its operand. If a bit is 0, it becomes 1, and if it's 1, it becomes 0.

   - Example: If you apply `~` to the binary representation of 5 (which is `0101` in 4 bits), you get `-6` (which is `1010` in 4 bits in two's complement representation).

   - It's used for bitwise negation.



2. `!` (Logical NOT Operator):

   - `!` is the logical NOT operator.

   - It's used in boolean logic, not bitwise operations.

   - It takes a boolean value (true or false) as an operand and returns the opposite boolean value.

   - Example: `!true` returns `false`, and `!false` returns `true`.

   - It's used for boolean negation, such as in conditional statements and logical expressions.



In summary, `~` is a bitwise operator used for inverting individual bits in a binary representation, while `!` is a logical operator used for boolean negation in conditional logic. They have different purposes and applications.



## Some Puzzles on Bit Manipulation

**Problem-1**



bitAnd - x&y using only ~ and |

 *   Example: bitAnd(6, 5) = 4

 *   Legal ops: ~ |

 *   Max ops: 8

 *   Rating: 1

```C

int bitAnd(int x, int y)

{



    int temp = ~(~x | ~y);

    return temp;

}

```

**Problem-2**



bitOr - x|y using only ~ and &

 *   Example: bitOr(6, 5) = 7

 *   Legal ops: ~ &

 *   Max ops: 8

 *   Rating: 1

```C

int bitOr(int x, int y)

{

    int temp = ~(~x & ~y);

    return 2;



}

```

**Problem-3**



isZero - returns 1 if x == 0, and 0 otherwise

 *   Examples: isZero(5) = 0, isZero(0) = 1

 *   Legal ops: ! ~ & ^ | + << >>

 *   Max ops: 2

 *   Rating: 1

```C

int isZero(int x)

{

    return !x;

}

```

**Problem-4**



minusOne - return a value of -1

 *   Legal ops: ! ~ & ^ | + << >>

 *   Max ops: 2

 *   Rating: 1

```C

int minusOne(void)

{

    return ~(1 << 31);

}

```

**Problem-5**



TMax - return maximum two's complement integer

 *   Legal ops: ! ~ & ^ | + << >>

 *   Max ops: 4

 *   Rating: 1

```C

int tmax(void)

{

    // Shift 1 to the left by 31 bits to set the sign bit to 0

    // All other bits will be set to 1

    return (1 << 31) ^ ~(1 << 31);

}

```

**Problem-6**



bitXor - x^y using only ~ and &

 *   Example: bitXor(4, 5) = 1

 *   Legal ops: ~ &

 *   Max ops: 14

 *   Rating: 2

```C

int bitXor(int x, int y) {

    int not_x = ~x;

    int not_y = ~y;

    int and_x_y = x & y;

    int and_not_x_not_y = not_x & not_y;

    int result = ~(and_x_y & and_not_x_not_y);

    return result;

}

```

**Problem-7**



getByte - Extract byte n from word x

 *   Bytes numbered from 0 (LSB) to 3 (MSB)

 *   Examples: getByte(0x12345678,1) = 0x56

 *   Legal ops: ! ~ & ^ | + << >>

 *   Max ops: 6

 *   Rating: 2

```C

int getByte(int x, int n)

{

    // Shift x right by 8 * n bits to get the desired byte in the least significant position

    int shifted = x >> (n << 3);



    // Mask the result to keep only the least significant byte

    int result = shifted & 0xFF;



    return result;

}

```

**Problem-8**



isEqual - return 1 if x == y, and 0 otherwise

 *   Examples: isEqual(5,5) = 1, isEqual(4,5) = 0

 *   Legal ops: ! ~ & ^ | + << >>

 *   Max ops: 5

 *   Rating: 2

```C

int isEqual(int x, int y)

{

    // XOR x and y, if they are equal, the result will be 0

    int result = !(x ^ y);



    return result;

}

```

**Problem-9**



negate - return -x

 *   Example: negate(1) = -1.

 *   Legal ops: ! ~ & ^ | + << >>

 *   Max ops: 5

 *   Rating: 2

```C

int negate(int x)

{

    // Negate x by taking its two's complement

    return (~x) + 1;

}

```

**Problem-10**



isPositive - return 1 if x > 0, return 0 otherwise

 *   Example: isPositive(-1) = 0.

 *   Legal ops: ! ~ & ^ | + << >>

 *   Max ops: 8

 *   Rating: 3



```C

int isPositive(int x)

{

    // Shift x 31 bits to the right to extract its sign bit

    int sign = (x >> 31) & 1;



    // If x is greater than 0, sign will be 0, and we negate it to get 1

    // If x is less than or equal to 0, sign will be 1, and we negate it to get 0

    return !sign;

}

```