$2$s Complement Arithmetic

Given the following decimal numbers:

A $=56$

B $=92$

C $=-24$

D $=-107$

Using $8-$bit two$$s complement arithmetic, perform the following six calculations as they

would be done on an $8-$bit microprocessor. Recall that subtraction is performed by

negating the second operand and adding, i$.$e$.$ all operations are performed with a binary

adder circuit.

$1.$ A$+$B

$2.$ A$-$B

$3.$ A$+$C

$4.$ A$-$C

$5.$ C$+$D

For each calculation, show the $8-$bit result $($and check that it corresponds to the correct

decimal value. Note any $$overflow$$ conditions $$ i$.$e$.$ the result is outside of the range of

values that can be represented by $8$ bits in an $8-$bit $2$s complement number system.

For example: $5-10=0000010100001010$

$=00000101+(-00001010)$

$=00000101+11110110$

$00000101$

$+11110110$

$=11111011$

$=-00000101$

$=-5$

This is the expected result, and is within the range of $8-$bit $2$s complement values