NIMCET 2012 — Computer PYQ

The correct answer is (a) 11000100.

Step 1: Convert $x$ and $y$ to Decimal

• For $y=00001010$:

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

  $$y=(2^3+2^1)=8+2=+10_{10}$$

• For $x=11111010$:

  Since the MSB is $1$, it is a negative number. To find its magnitude, take the 2's complement:

  1's complement of $11111010$ is $00000101$.

  Adding $1$: $00000101+1=00000110$.

  Magnitude $=(2^2+2^1)=4+2=6$.

  $$x=-6_{10}$$

Step 2: Calculate the Product in Decimal

Step 3: Convert $-60$ back to 8-bit 2's Complement

• Binary of $+60$:

  $$60=32+16+8+4=(00111100{)}_2$$

• 1's complement: $11000011$

• 2's complement (Add $1$):

  $$11000011+1=11000100$$

Final 8-bit product is $11000100$.