Question

Let $A=11111010$ and $B=0001010$ be two 8 bit 2's complement numbers. Their product in 2's complement is

Answer 1

$A=11111010$
$=-2^{7\times }1+2^6\times 1\times 2^5\times 1+2^4\times 1+2^3\times 1+2^2\times 0+2^1\times 1+2^0\times 0$
$=-128+64+32+16+8+2$
$=-128+122$
$=-6$
$B=00001010=2^6\times 1+2^1\times 1=8+2=10$

$AB=(-6)\times 10=-60$

So the value of AB in 2's complement representation is

$AB=11000100$