Which inputs on a half-adder circuit will produce a sum of 0 and a carry of 1?

In a half-adder circuit, two binary inputs are processed to produce two outputs: sum and carry. The sum output represents the result of the binary addition of the inputs, while the carry output indicates if there is an overflow beyond the least significant bit.

To achieve a sum of 0 and a carry of 1, it is essential to understand the behavior of binary addition. The sum is calculated by performing an exclusive OR operation, meaning that the sum is only 1 if one and only one of the inputs is 1. The carry output is determined by an AND operation, which provides a carry of 1 when both inputs are 1.

In the case where both inputs A and B are 1, the sum will be 0 (because 1 XOR 1 equals 0) and the carry will be 1 (since 1 AND 1 equals 1). Therefore, this condition perfectly meets the requirement of producing a sum of 0 and a carry of 1.

The other combinations offered as choices produce varying results that do not satisfy the requirements for both outputs. For instance, when both A and B are 0 or when one input is 1 and the other is 0, the sum will result in