NIMCET 2008 — Computer PYQ

Step 1: Convert $A$ to Decimal

$A=11111010$. Since the MSB (Most Significant Bit) is 1, it is a negative number.

To find its magnitude, take the 2's complement of $A$:

1. Invert the bits: $00000101$

2. Add 1: $00000101+1=00000110$

3. $00000110_2=6_{10}$

   So, $A=-6$.

Step 2: Convert $B$ to Decimal

$B=00001010$. Since the MSB is 0, it is a positive number.

$B=(1\times 2^3)+(1\times 2^1)=8+2=10$.

So, $B=10$.

Step 3: Multiply the Decimal Values

Step 4: Convert $-60$ back to 8-bit 2's Complement

1. Find the binary for $+60$:

   $60=32+16+8+4$

   Binary: $00111100$

2. Take the 1's complement (invert bits):

   $11000011$

3. Add 1 to get the 2's complement:

   $11000011+1=11000100$

Verification:

The result $11000100$ represents:

$-128+64+4=-64+4=-60$.

This matches our calculated decimal product.

Final Answer:

The correct option is (a) $11000100$.