Final answer:
In binary addition/subtraction of 4-bit 2's complement numbers, correctness can be checked by comparing carry into and out of the most significant bit. An XOR gate can be used to detect overflow, with its output flagging an incorrect result if high. This method works for both addition and subtraction.
Step-by-step explanation:
When performing binary addition or subtraction using 2's complement numbers, we can determine the correctness of the result by checking for overflow. An overflow occurs when the algorithm produces a result which is outside the range of values that can be represented with the number of bits used. In 4-bit binary numbers, this can happen when adding two positive numbers results in a negative number, or when adding two negative numbers gives a positive result.
To detect overflow, one should examine the carry into the most-significant bit (C4) and the carry out (C5). If these carries are not the same, it indicates an overflow has occurred. Using logic gates, one could implement this check by creating an XOR gate, as it outputs a 1 when the inputs are different. Connect the C4 and C5 to an XOR gate, and the output will be 1 if there is an overflow, indicating an incorrect result.
In subtraction, which is done by adding the two's complement of the number to be subtracted, the same principles apply. However, one must also be aware of the sign change in the number being subtracted before performing the addition.
Binary subtraction follows similar rules where you change the sign of the subtracted number and then proceed with binary addition. The check for overflow is the same as with addition.