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

$\{$:$x+[Y{]}^{**}).$ 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 ${1101}_2-{0111}_2.$

$1101-,1101,1101$

$-0111-2C+-[0111{]}^{**}=\frac{+1001}{\frac{1}{0110}}$;$2C$ converts subtract $to$ add

Calculate $-4_{10}-(2{)}_{10},$ using binary subtraction.

$-4=-0100-2C=[0100{]}^{**}=1100$;$2Cto$ get $-4$ into $S2C$ form

$-2_{?}=-0010-2C+{[}_{{?}_{?}}0010{]}^{**}=\frac{+1110\text{;}}{\frac{1}{1010}}2C$ converts subtract $to$ add

Now you try!

a$.{0101}_2-{1010}_2$

b$.{1101}_2-{0110}_2$

c$.-9_{10}-4_{10}$

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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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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

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 ${1100}_2-{0010}_2.$

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

overflow