Need clarification regarding carry and overflow bit

[leo255]

I'm trying to understand carry & overflow bits. Carry seems pretty easy - If I'm not mistaken, if you carry on your last bit into a bit that you don't have, the carry flag is set to 1.

For overflow, I referred to another previous thread on here, of which one of the posters recommended the thread-starter look at the following link:

http://teaching.idallen.com/dat2343/00s/overflow.txt

This was very helpful to me, by clarifying that the overflow bit is the exclusive or (XOR), and is set to 1 when either (but not both) of the last bit or carry bit has a 1 carried into it. When they both have a 1 carried into them, it is set to 0.

I feel like I understand how to determine the overflow bit, but I don't understand what it means. The carry bit is easy: you are adding two numbers, and just don't have enough room (enough bits), so you don't get an accurate representation of the number. Just trying to get the same understanding for the overflow bit.

Thanks in advance for the help.

 

[jedishrfu]

The last bit is considered to be the sign bit and so an addition overflow results in a possible sign reversal.

http://en.m.wikipedia.org/wiki/Overflow_flag

 

[mfb]

Carry is mainly used for unsigned integers, overflow is something similar for signed integers.

If you add 0100 + 0101 (let's use4 bits here), you expect a positive result because both numbers are positive. Simply putting them into your CPU will give 1001, however - that number is negative. The carry bit is not set (as both numbers are positive) but the first bit got set -> overflow.

In the same way, adding two negative numbers should give a negative result.
Adding 1100 and 1100 gives (1)0100 where (1) is carry - a positive result! Carry bit is set, but the first bit is not -> overflow

The two cases for subtraction can be studied in the same way.

 

[rcgldr]

Carry is set for unsigned addition. For unsigned subtraction, it's usually a "borrow" bit, but on some processors it's the "not borrow" bit.

Overflow is for signed addition or subtraction, and indicates that the sign of the result is wrong due to overflow (addition) or underflow (subtraction). For a signed or unsigned multiply with a double register product, overflow isn't possible. For a signed or unsigned divide with a double register dividend and single register quotient, the quotient can overflow (including division by 0).

 

[rezeew]

Hello,

Thank you for reaching out for clarification on the concepts of carry and overflow bits. As you mentioned, the carry bit is set to 1 when there is a carry from the last bit into a bit that does not exist. This indicates that the result of the addition or subtraction operation is too large to be represented accurately within the given number of bits.

On the other hand, the overflow bit is set to 1 when there is a mismatch between the signs of the numbers being added or subtracted. This means that the result of the operation is not within the range of values that can be represented by the given number of bits. For example, if you are working with 8-bit numbers and the result of an addition operation is 255 (11111111 in binary), the overflow bit will be set to 1 because this value cannot be represented in 8 bits without losing the sign bit.

In summary, the carry bit indicates that the result is too large to be represented accurately, while the overflow bit indicates that the result is outside of the range of values that can be represented. I hope this helps to clarify the concept for you. If you have any further questions, please let me know.