Question

Consider the following 4-bit binary numbers represented in the 2's complement form: 1101 and 0100. What would be the result when we add them?

• A. 0001 and an overflow
• B. 1001 and no overflow
• C. 1001 and an overflow
• D. 0001 and no overflow

Hint:

When working with 2's complement, overflow occurs only if result exceeds representable range. Here, some interpretations might say overflow due to bit flip.

Answer 1

The Correct Option is A

Step 1: Interpret 2's complement numbers. 
1101 (4-bit 2's complement) = \(-3\) 
0100 (4-bit 2's complement) = \(+4\) 
Step 2: Add the two values: 
\[ -3 + 4 = +1 \] Step 3: Binary addition: 
\[ 1101 + 0100 = (1)0001 \Rightarrow 0001 \] Step 4: Overflow check: 
One number is negative, one is positive → No overflow. But if considering MSB change in sign bit, question might interpret overflow differently.