$1.(10$ points$)$ Consider the following two $8-$bit input operands: $101111002$ and $110111002.$ a$)$ Add these numbers using the binary addition algorithm, and showing all intermediate carry bits. b$)$ Truncate the result to $8$ bits, and translate both input operands and the result of the addition into decimal, interpreting the bit sequences as $8-$bit unsigned integers. Does the addition cause overflow? Why? c$)$ Translate both input operands and the truncated result into decimal, interpreting the bit sequences as $8-$bit signed integers in two's complement representation. Does the addition cause overflow? Why?