Question $1$:

$($a$)$ Find the range of unsigned decimal integers that can be stored in a dword.

$($b$)$ Find the range of signed decimal integers $($smallest to largest$)$ that can be stored in $2$s complement form in a dword.

Question $2$: Perform the addition operation, giving the sum in hex using the

same number of hex digits as the original two operands; State whether or not overflow and carry occur; Interpret the operations as $2$s complement signed and convert the problem to the equivalent decimal problem; Verify that the signed interpretation is correct when there is no overflow; Interpret the operands as unsigned and convert the problem to the equivalent decimal problem; Verify that the unsigned interpretation is correct when there is no carry.

$2$A $44+$ D$9$ CC

Question $3$: Instructions are the same as in Question $2$ but repeat them for $5$E $+4$B$.$

Question $4$: Consider the byte length $2$s complement representation and show

that FF is $-1.$ Now consider the word length $2$s complement representation of FF FF and show that it is also $-1.$

Question $5$: We learned how to take the $2$s complement of a number by

subtracting it from an appropriate power of $2.$ An alternative method is to write the

number in binary $($using the correct number of bits for the length of the representation$),$ change each $0$ bit to $1$ and each $1$ bit to $0($this is called $$taking the $1$s complement$),$ and then adding $1$ to the result $($discarding any carry into an extra bit$).$ Show that these two methods are equivalent.

Note: It is not sufficient to show that these two approaches are the same by using an

particular example. You should take an arbitrary n$-$bit binary number and argue.