$1\text{'}$s$-$ and $2\text{'}$s$-$complement number systems a$.$ Prove that

$,$ where the superscript $"$

$"$ denotes any complementation scheme. b$.$ Find the difference between the two binary numbers $0010$ and $0101$ in two ways: First by adding the $2\text{'}$s complement of $0101$ to $0010,$ and then by using the equality of part a$,$ where $"$

denotes bitwise complementation. Compare the two methods with regard to their possible advantages and drawbacks.

$1\text{'}$s$-$ and $2\text{'}$s$-$complement number systems

a$.$ Prove that

$,$ where the superscript $"$

$"$ denotes any complementation scheme.

b$.$ Find the difference between the two binary numbers $0010$ and $0101$ in two ways: First by adding the $2\text{'}$s complement of $0101$ to $0010,$ and then by using the equality of part a$,$ where $"$

denotes bitwise complementation. Compare the two methods with regard to their possible advantages and drawbacks.