To perform additions with the $2$s complement representation, which of the following mechanisms should be adopted to produce correct results $?$

$($a$)$ Signs of both operands should be recorded to determine the sign of the result

$($b$)$ Sign of the result should be flipped to the opposite when there is a carry out of the

sign bit

$($c$)$ Adding $7$ to the LSB of the result when there is a carry out of the sign bit

$($d$)$ Except the sign bit, flipping all the bits of the result to the opposite when there is a

carry out of the sign bit

$($e$)$ Any carry out of the sign bit should be ignored