def add_with_flags(a, b):
    """
    Performs 32-bit addition with carry and overflow flag calculation
    Simulates ALU addition operation with status flags
    """
    # Calculate the sum and mask to 32 bits (simulate 32-bit register)
    result = (a + b) & 0xFFFFFFFF
    
    # Carry flag: set when addition exceeds 32-bit unsigned range
    carry  = 1 if (a + b) > 0xFFFFFFFF else 0
    
    # Extract sign bits (bit 31) for overflow detection
    sign_a = (a >> 31) & 1        # Sign bit of operand A
    sign_b = (b >> 31) & 1        # Sign bit of operand B  
    sign_r = (result >> 31) & 1   # Sign bit of result
    
    # Overflow flag: set when signed addition overflows
    # Occurs when: same sign inputs produce different sign output
    overflow = 1 if (sign_a == sign_b) and (sign_r != sign_a) else 0
    
    return result, carry, overflow

# Test cases demonstrating different flag conditions
tests = [
    (0x7FFFFFFF, 0x01),      # Max positive + 1 → signed overflow
    (0xFFFFFFFF, 0x01),      # Max unsigned + 1 → carry (wrap to 0)
    (0x80000000, 0x80000000), # Min negative + min negative → signed overflow
    (0x12345678, 0x87654321), # Regular addition → no flags
    (0x00000000, 0x00000000), # Zero + zero → no flags
]

print("32-bit Addition with Status Flags")
print("=" * 50)
print("Input A    + Input B    = Result     C V")
print("-" * 50)

for a, b in tests:
    r, c, v = add_with_flags(a, b)
    print(f"{a:#010x} + {b:#010x} = {r:#010x}  {c} {v}")

print("\nLegend:")
print("C = Carry flag (unsigned overflow)")
print("V = Overflow flag (signed overflow)")