Overflow Conditions

Question

Please correct if any of the following does not represnt overflow condition when two binary 2s complement digits are added
 

1. Two +ve (sign bit 0) numbers are added result is -ve ( sign bit becomes 1)
2. Two -ve (sign bit 1) numbers are added result is +ve ( sign bit becomes 0)
3. Carry from MSB  $\oplus$ Carry into MSB = 1
4. When we add two unsigned numbers there is an out Carry C _out

Comments

First 3 are true but i'm not getting 4th option

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All correct.

for option 4^th adding 1000 and 1001 gives us 10001, carry = 1, and data on 4-bit register = 0001. Thus Overflow occurs. and it can be seen for all cases, whenever addition of two unsigned numbers yields a carry.

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ALL true for "OVERFLOW"

Answer 1

1) ${\color{Blue} 0} (C_{in}) 1001$=9

    ${\color{Blue} 0} (C_{in}) 1000$=8

$----------------------$

       ${\color{Blue} 1}0001$=17

Here Before addition sign bit=0

After addition sign bit=1

Carry (C_{in})=0

Overflow(C_{out})=1

2) ${\color{Blue} 1} (C_{in}) 1000$= -8

    ${\color{Blue} 1} (C_{in}) 1001$= -7

$----------------------$

       ${\color{Blue} 1}0001$= -15

Here Before addition sign bit=1

After addition sign bit=1

Carry (C_{in})=1

Overflow(C_{out})=1

3) same as 1

in eg. 1)$C_{in}\oplus C_{out}=1$

So, overflow occurs

  

4) Say, take two 4 bit number addition (like +14,+15)

After addition it takes more than 4 bits (out of range)

Then there is a overflow

Comments

Case(1). Correction : $C_{in} = 1$ and $C_{out} = 0$, hence Overflow

You have taken 5-bit numbers and added them and overflow occurs But $C_{out}$ (Carry out of MSB while addition) alone can not tell whether overflow occurs or not (in 2's complement addition).

Case(2). $C_{in} = 1$ and $C_{out} = 1$, hence NO Overflow

There is no Overflow in $2^{nd}$ case. In 5-bits, we can store $-16$ to $+15$ in 2's complement format. So, Adding -8 and -7 will not cause Overflow. Again, $C_{out}$ (Carry out of MSB while addition) alone can not tell whether overflow occurs or not (in 2's complement addition).

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Case 2 also cause an overflow

https://www.doc.ic.ac.uk/~eedwards/compsys/arithmetic/index.html

right?

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Case 2 also cause an overflow

Case 2 in your answer (not referring to the 2nd statement of the Question) doesn't cause Overflow because You have taken 5-bit numbers. 

And one more thing that "Carry bit" is defined for the addition, Not for the numbers being added. So, What does $C_{in}$ means in the Numbers being added i.e. in Augend/Addend.

Answer 2

In all the 4 conditions overflow will occur .