$14.$ Determine the result of the following binary subtraction calculations $($including the result carry bit$)$ using the binary addition method and the two$$s complement of the subtrahend $($X$-$Y $=$ X$+[$Y$]*).$ Do not worry about overflows or the final result in decimal; we$$ll look at those in the final problems of this homework. Subtraction is performed the same way regardless if the values are in S$2$C form or not; that only impacts decisions of overflow.

Here are some examples:

Calculate $1101201112.$

$1101--->11011101$

$-0111-2$C$->+[0111]*=+1001$; $2$C converts subtract to add

$1|0110$

Calculate $-410(2)10,$ using binary subtraction.

$-4=-0100-2$C$->[0100]*=1100$; $2$C to get $-4$ into S$2$C form

$-2=-0010-2$C$->+[0010]*=+1110$; $2$C converts subtract to add

$1|1010$

Now you try!

a$.0101210102$

b$.1101201102$

c$.-910-410$

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$15.$ For the two examples in Problem $14($the examples, not the problems in a$),$ b$),$ c$)),$ determine:

a$.$ if unsigned overflow occurred. Hint: just like addition, unsigned overflow is identified by the result carry, but opposite of addition, in subtraction carry $=0$ indicates overflow

b$.$ if signed overflow occurred. Hint: the rules for signed overflow are different for subtraction than addition, but they are also intuitive

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$16.$ Finally, let$$s explore if the results and overflow indicators calculated in Problems $14$ and $15$ make sense. For the two cases in a$)$ and b$)$ below, use the tables of binary values in the textbook or course notes to determine the decimal values of the inputs and the result $($ignoring carry$).$ Then comment on how these compare to the overflow results you identified in Problem $15.$

a$.$ Assuming the input values and results are in unsigned form; compare to unsigned overflow. Hint: for the second example, assume the binary input is $1100200102.$

b$.$ Assuming the input values and results are in signed $($S$2$C$)$ form; compare to signed overflow