NIMCET 2008 — Computer PYQ

To find the product of two signed numbers in 2's complement, the most efficient method is to convert them to decimal, multiply, and then convert the result back to 8-bit 2's complement.

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) $11000100$.