$[12$ marks$]$ For this question, assume you working with $10-$bit sequences using two's

complement representation for integers.

Show your work for all calculations. You may directly convert to and from positive

decimal integer values and bit sequences representing binary numbers. For

example, you may go directly from ${15}_{10}$ to $0000001111$ without showing any

additional steps.

For questions that require calculations where the arguments are bit sequences

the answers must be bit sequences. The work of your solutions may not convert

the values to decimal numbers. You may do those conversions yourself to check

your answers.

Clearly indicate any calculation with a result that causes an overflow.

$($a$)$ What is the bit sequence that represents the decimal integer $-375?$

$($b$)$ What is the decimal value of $1101010011?$

$($c$)$ What is the sum of the bit sequences: $1000101001+1000011011?$

$($d$)$ What is the sum of the bit sequences: $0101101001+0110101011?$

$($e$)$ What is the sum of the bit sequences: $1101100101+1111101011?$

$($f$)$ What is the difference of the bit sequences: $0001010010-0101100100?$

$($g$)$ What is the difference of the bit sequences: $0101101001-1000011010?$