feat(boolean_algebra): add half adder Implementation

.gitignore

@@ -108,3 +108,4 @@ venv.bak/
 .try
 .vscode/
 .vs/
+scripts/python3.bat

boolean_algebra/full_adder.py

@@ -0,0 +1,67 @@
+"""
+A Full Adder is a fundamental combinational circuit in digital logic.
+It computes the sum and carry outputs for two input bits and an input carry bit.
+
+Truth Table:
+    -----------------------------------------
+    | A | B | Cin | Sum | Cout |
+    -----------------------------------------
+    | 0 | 0 |  0  |  0  |   0   |
+    | 0 | 1 |  0  |  1  |   0   |
+    | 1 | 0 |  0  |  1  |   0   |
+    | 1 | 1 |  0  |  0  |   1   |
+    | 0 | 0 |  1  |  1  |   0   |
+    | 0 | 1 |  1  |  0  |   1   |
+    | 1 | 0 |  1  |  0  |   1   |
+    | 1 | 1 |  1  |  1  |   1   |
+    -----------------------------------------
+
+Refer:
+https://en.wikipedia.org/wiki/Adder_(electronics)#Full_adder
+"""
+
+
+def full_adder(a: int, b: int, cin: int) -> tuple[int, int]:
+    """
+    Compute the sum and carry-out for a Full Adder.
+
+    Args:
+        a: First input bit (0 or 1).
+        b: Second input bit (0 or 1).
+        cin: Carry-in bit (0 or 1).
+
+    Returns:
+        A tuple `(sum_bit, carry_out)`.
+
+    >>> full_adder(0, 0, 0)
+    (0, 0)
+    >>> full_adder(0, 1, 0)
+    (1, 0)
+    >>> full_adder(1, 0, 0)
+    (1, 0)
+    >>> full_adder(1, 1, 0)
+    (0, 1)
+    >>> full_adder(0, 0, 1)
+    (1, 0)
+    >>> full_adder(1, 1, 1)
+    (1, 1)
+
+    Raises:
+        ValueError: If any input is not 0 or 1.
+    """
+    if a not in (0, 1) or b not in (0, 1) or cin not in (0, 1):
+        raise ValueError("Inputs must be 0 or 1.")
+
+    # Sum is XOR of the inputs
+    sum_bit = a ^ b ^ cin
+
+    # Carry-out is true if any two or more inputs are 1
+    carry_out = (a & b) | (b & cin) | (a & cin)
+
+    return sum_bit, carry_out
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

boolean_algebra/half_adder.py

@@ -0,0 +1,54 @@
+"""
+A Half Adder is a basic combinational circuit in digital logic.
+It computes the sum and carry outputs for two input bits.
+
+Truth Table:
+    -------------------------
+    | Input A | Input B | Sum | Carry |
+    -------------------------
+    |    0    |    0    |  0  |   0   |
+    |    0    |    1    |  1  |   0   |
+    |    1    |    0    |  1  |   0   |
+    |    1    |    1    |  0  |   1   |
+    -------------------------
+
+Refer - https://en.wikipedia.org/wiki/Adder_(electronics)#Half_adder
+"""
+
+
+def half_adder(input_a: int, input_b: int) -> tuple[int, int]:
+    """
+    Compute the sum and carry for a Half Adder.
+
+    Args:
+        input_a: First input bit (0 or 1).
+        input_b: Second input bit (0 or 1).
+
+    Returns:
+        A tuple `(sum_bit, carry_bit)`.
+
+    >>> half_adder(0, 0)
+    (0, 0)
+    >>> half_adder(0, 1)
+    (1, 0)
+    >>> half_adder(1, 0)
+    (1, 0)
+    >>> half_adder(1, 1)
+    (0, 1)
+
+    Raises:
+        ValueError: If inputs are not 0 or 1.
+    """
+    if input_a not in (0, 1) or input_b not in (0, 1):
+        raise ValueError("Inputs must be 0 or 1")
+
+    sum_bit = input_a ^ input_b
+    carry_bit = input_a & input_b
+    return sum_bit, carry_bit
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+