To add the two's complement binary numbers 0101 and 1001, align and add the digits to get 1110, keeping in mind that any overflow beyond the fourth bit is ignored. The binary result '1110' corresponds to the decimal number -2.
The question involves adding two binary numbers given in two's complement notation. When adding the four-bit binary numbers 0101 (which represents the decimal number 5) and 1001 (which represents the decimal number -7, as it is in two's complement form), we line up the bits and add, paying special attention to bit carrying:
0101+1001---- 1110
The result is the binary number 1110, which in two's complement notation represents the decimal number -2. The addition operation in binary follows the same commutative principle as decimal numbers, such that A + B = B + A. However, noting that we are dealing in four bits, if any carrying beyond the fourth bit occurs, it would normally be ignored (this is known as an overflow), but since our result still fits within four bits, no overflow is present here.
Binary addition also follows rules similar to decimal addition: adding two positive or two negative numbers will result in a number with the respective sign, while adding numbers of opposite signs involves a subtraction process.