In a half-adder circuit, which input combination results in a sum of 0 and a carry of 1?

In a half-adder circuit, the purpose is to perform binary addition on two single-bit inputs, A and B. The two outputs from a half-adder are the sum and the carry.

When both A and B are 1, the sum output will be 0 because, in binary addition, 1 + 1 equals 10. The least significant bit (the sum bit) is 0, and a carry is generated, which represents the next higher bit in the binary addition—hence, the carry output is 1.

This accurately reflects the behavior of a half-adder:

• Sum = A XOR B

• Carry = A AND B

In this specific input combination (A = 1, B = 1), we can confirm:

• The sum calculation: 1 XOR 1 = 0

• The carry calculation: 1 AND 1 = 1

Thus, the combination leading to a sum of 0 and a carry of 1 occurs solely when both A and B are set to 1.