End-around carry in one’s complement arithmetic: In one’s complement addition/subtraction, if an end carry is generated beyond the most significant bit, that 1 is added back into the least significant bit. Assess this definition.

Introduction / Context:
One’s complement is an older signed-number system where negative numbers are formed by inverting all bits. Arithmetic in one’s complement uses the “end-around carry” rule to restore a correct result whenever an addition produces a carry out of the most significant bit.

Given Data / Assumptions:

• Fixed-width one’s complement representation.
• We perform addition of bit patterns and may apply an end-around carry if one occurs.
• Subtraction can be implemented as addition of the one’s complement of the subtrahend.

Concept / Approach:
If an addition creates a carry out of the MSB, that carry represents a wrap-around in modulo arithmetic. In one’s complement, you add that single carry bit back into the least significant bit of the sum to obtain the final, corrected result. This distinguishes it from two’s complement, where the final carry is discarded.

Step-by-Step Solution:

Verification / Alternative check:
Example (4-bit): 0101 (+5) + 1010 (−5) = 1111 with no end carry → represents −0; with 0111 (+7) + 0100 (+4) = 1011 and end carry 1 → add to LSB yields 1100 (+11), correct.

Why Other Options Are Wrong:
“Invalid” contradicts the core rule of one’s complement arithmetic. Two’s complement and BCD follow different rules (carry is discarded in two’s complement, and BCD uses digit-wise corrections).

Common Pitfalls:
Mixing one’s and two’s complement rules; forgetting the final add-back of the end carry results in an off-by-one error.

Final Answer:
Valid