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The bitwise calculator is a tool to perform operations like AND, OR, XOR, NOT, NAND, NOR, and Shift bits on numbers. The input can combine binary, decimal, hexadecimal, or octal numbers.

To use this calculator, follow the below steps:

- Enter the number in the first input box.
- Select the operator in the dropdown list (+, – *, / , &, |, XOR, ~, NAND, NOR, <<, >>)
- Enter the number in the second input box.
- You will see the calculated number in the output boxes for each base system
- The results is displayed as binary, decimal, hexadecimal, or octal numbers.

- A wide variety of programming languages supports bitwise operations on two integer integers.
- The evaluation and manipulation of particular bits within an integer are possible with bitwise operators.
- Each subsequent pair of bits in the operands is subjected to the operation.
- Bitwise AND, OR, and XOR are the three most popular operations.

A base system is a mechanism of representing numbers. When we talk about base-n, the system can show a number with n characters (including 0). Numbers are represented by digits that are less than or equal to n. As a result, 3 in base-3 equals 10: because that system lacks a "3," it starts anew (1, 2, 10, 11, 12, 20, 21, 22, 100, etc.).

We commonly utilize base-10 since we have 10 (including 0) digits until we start anew (8,9,10). We only have two characters in base-2 (binary), 0 and 1, until we begin anew. In our (base-10) system, the binary number 10 is 2 in this example.

Operator | Name | Description |
---|---|---|

& | AND | Sets each bit to 1 if both bits are 1 |

| | OR | Sets each bit to 1 if one of two bits is 1 |

^ | XOR | Sets each bit to 1 if only one of two bits is 1 |

~ | NOT | Inverts all the bits |

<< | Zero fill left shift | Shifts left by pushing zeros in from the right and let the leftmost bits fall off |

>> | Signed right shift | Shifts right by pushing copies of the leftmost bit in from the left, and let the rightmost bits fall off |

>>> | Zero fill right shift | Shifts right by pushing zeros in from the left, and let the rightmost bits fall off |

Bitwise calculation refers to manipulating and operating individual bits within binary data representations. In computing, binary digits, or bits, are the fundamental information units that can be either 0 or 1.

Bitwise calculations involve applying logical or arithmetic operations to these individual bits rather than simultaneously operating on the entire binary number.

Common bitwise operations include:

- Bitwise AND (&): Compares two bits and returns 1 if both bits are 1; otherwise returns 0.
- Example: 5 (0101) & 3 (0011) = 1 (0001)
- Bitwise OR (|): Compares two bits and returns 1 if either bit is 1; otherwise returns 0.
- Example: 5 (0101) | 3 (0011) = 7 (0111)
- Bitwise XOR (^): Compares two bits and returns 1 if the bits are different; otherwise returns 0.
- Example: 5 (0101) ^ 3 (0011) = 6 (0110)
- Bitwise NOT (~): Flips the bits, changing 0 to 1 and 1 to 0.
- Example: ~5 (0101) = -6 (1010) (assuming a two's complement representation)

Depending on the context, these operations can be performed on individual bits or entire binary numbers. Bitwise calculations are commonly used in low-level programming, such as manipulating hardware registers, performing bitwise flags, or optimizing specific algorithms. They allow for efficient manipulation of binary data at a low level.

We have to stop optimizing for programmers and start optimizing for users.

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