Question

In the following problems, assume you are using 2s complement form and do the indicated operation. Leave the answers in binary. Also, assume you are dealing with signed numbers.

Also, assume we are saving the answer in a 8-bit register. In this case, for each problem would the saved answer be correct. If not for which of the following problems would if be incorrect and why?

1.   6 + 7
2.   6 + (-7)
3.    -6 + 13 (Note: 13, which is positive in binary needs 4 bits and is 0111, -6 in 2’s complement form is done as follows: 6 = 0110, now change all bit in 6 and add 1 to get 1010 = -6 in 2s complement form. It is important to notice that 6 in bold above is positive and must start with a 0. So, we couldn’t write 6 initially as 110 and then change it to 2s-complement. That is, since we are dealing with signed numbers each must start with a 0 or 1 to show its sign.)
4. -6 – (-7)
5. -70 – 80 (In this example, What would the Overflow Flag (OF) be and how did it get this value.)

Answer 1

(-70+(-80))

Here -70 & 80 subtracted

(70)₁₀=(01000110)₂

(-70)₁₀=(10111010)₂ ----by 2'complement

(80)₁₀=(01010000)₂

(-80)₁₀=(10110000)₂

Add(-70 & -80)

10111010

+ 10110000

--------------------------

1] 01101010

When 2'complement is taken

10010110 (-150)

Overflow flag indicates that the result is too large to fit in 8 bit.OF is 1when the following conditions satisfies.

When the two +ve operands are added there results should exceed127

When the two -ve operand are subtracted there result should be less than -128

OF=1 because the result is less than -128 i.e -150