# Bitwise And¶

The Bitwise And (denoted as '&') is implemented by applying the following truth table

a b a & b
0 0 0
0 1 0
1 0 0
1 1 1

between each pair of qubits in register A and B (or qubit and bit).

Note that integer and fixed-point numbers are represented in a 2-complement method during function evaluation. The binary number is extended in the case of a register size miss-match. For example, the positive signed number $$(110)_2=6$$ is expressed as $$(00110)_2$$ when operating with a 5-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

## Syntax¶

Function: BitwiseAnd

Parameters:

{
"function": "BitwiseAnd",
"function_params": {
"left_arg": 3,
"right_arg": {
"size": 3
}
}
}


### Register Names¶

By default, the input registers are called left_arg and right_arg. If the name field of a RegisterUserInput object is specified, then the name of the register is determined accordingly. If one of the arguments is a constant then it is not available as an input register.

The output registers include the result register. By default, it is called bitwise_and, but its name may be overridden by the output_name argument. In addition, since the computation is done out-of-place, input registers are also available as output registers, with the same names.

### Example 1: Two Register¶

    {
"logic_flow": [
{
"function": "BitwiseAnd",
"function_params": {
"left_arg": {"size": 5, "is_signed":true},
"right_arg": {"size": 3}
}
}
]
}

from classiq import ModelDesigner
from classiq.builtin_functions import BitwiseAnd
from classiq.interface.generator.arith.arithmetic import RegisterUserInput

params = BitwiseAnd(
left_arg=RegisterUserInput(size=5, is_signed=True),
right_arg=RegisterUserInput(size=3),
)
model_designer = ModelDesigner()
model_designer.BitwiseAnd(params)
circuit = model_designer.synthesize()


This example generates a circuit that performs bitwise 'and' between two registers. The left arg is signed with 5 qubits and the right arg is unsigned with 3 qubits.

### Example 2: Integer and Register¶

    {
"logic_flow": [
{
"function": "BitwiseAnd",
"function_params": {
"left_arg": 3,
"right_arg": {"size": 3}
}
}
]
}

from classiq import ModelDesigner
from classiq.builtin_functions import BitwiseAnd
from classiq.interface.generator.arith.arithmetic import RegisterUserInput

params = BitwiseAnd(left_arg=3, right_arg=RegisterUserInput(size=3))
model_designer = ModelDesigner()
model_designer.BitwiseAnd(params)
circuit = model_designer.synthesize()


This example generates a circuit that performs bitwise 'and' between a quantum register and an integer. The left arg is an integer equal to three and the right arg is unsigned quantum register with 3 qubits.