> ## Documentation Index
> Fetch the complete documentation index at: https://prod-mint.classiq.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Bitwise And

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  Open this notebook in GitHub to run it yourself
</Card>

The Bitwise And (denoted as '&') is implemented by applying this truth table between each pair of qubits in register A and B (or qubit and bit).

<center>| a | b | a & b | | :-: | :-: | :---: | | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 |</center>

Note that integer and fixed-point numbers are represented in a two-complement method during function evaluation.

The binary number is extended in the case of a register size mismatch.

For example, the positive signed number $(110)_2=6$ is expressed as $(00110)_2$ when operating with a five-qubit register.
Similarly, the negative signed number $(110)_2=-2$ is expressed as $(11110)_2$.

Examples:

5 & 3 = 1 since 101 & 011 = 001

5 & -3 = 5 since 0101 & 1101 = 0101

-5 & -3 = -7 since 1011 & 1101 = 1001

## Examples

#

### Example 1: Two Quantum Variables

This example generates a quantum program that performs a bitwise 'and' between two variables, both are unsigned integer

```python theme={null}
from classiq import *


@qfunc
def main(a: Output[QNum], b: Output[QNum], res: Output[QNum]) -> None:
    a |= 4
    b |= 5
    res |= a & b


qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)

result = execute(qprog).result_value()
result.parsed_counts
```

<Info>
  **Output:**

  ```
  [{'a': 4.0, 'b': 5.0, 'res': 4.0}: 1000]
    

  ```
</Info>

#

### Example 2: Integer and Quantum Variable

This example generates a quantum program that performs a bitwise 'and' between a quantum variable and an integer.

The left arg is an integer equal to 3
and the right arg is an unsigned quantum variable with three qubits.

```python theme={null}
@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
    a |= 5
    res |= 3 & a


qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)

result = execute(qprog).result_value()
result.parsed_counts
```

<Info>
  **Output:**

  ```
  [{'a': 5.0, 'res': 1.0}: 1000]
    

  ```
</Info>