NIMCET 2008 — Computer PYQ

To solve this, we perform binary addition and then check the overflow condition for signed 2's complement numbers.

Step 1: Perform Binary Addition

We add the two 4-bit numbers:

Calculation:

  11   (Carries)
  1101
+ 0100
-------
 10001

The result of the addition is $10001$. Since we are working with 4-bit numbers, we discard the carry-out from the most significant bit (MSB), leaving us with the 4-bit result: $0001$.

Step 2: Check for Overflow

In 2's complement arithmetic, an overflow occurs only in two specific cases:

1. Positive + Positive = Negative (MSB of both inputs is 0, but MSB of result is 1).

2. Negative + Negative = Positive (MSB of both inputs is 1, but MSB of result is 0).

Let's check our MSBs:

• First number ($1101$): MSB is 1 (Negative)

• Second number ($0100$): MSB is 0 (Positive)

Rule: Adding a positive number and a negative number never results in an overflow, regardless of the carry-out.

Step 3: Verification with Decimal Values

• $1101$ in 2's complement: The decimal value is $-8+4+0+1=-3$.

• $0100$ in 2's complement: The decimal value is $4$.

• Expected Sum: $-3+4=+1$.

• Binary $0001$ in 2's complement is +1.

Since the result (+1) fits perfectly within the 4-bit range ($-8$ to $+7$), there is no overflow.

Final Answer:

The correct option is (c) $0001$ and no overflow.