I am working on Subtractor circuits using Adder circuits. I have to do x-y.

Suppose x = 111111 , y = 100000 Using the 6 bit adder circuit I created the overflow flag is coming to be 0 but when I solve it using pen and paper the overflow is coming to be 1.

When x = 000000 and y = 000000 the Carry out flag is coming to be 1 but using pen and paper it is coming to be 0.

I have used the basic logic used to create Adder circuits and for evaluation of flags.

I created 15 test cases. Only these two test cases did not agree with these flags. The final answer they displayed was correct.

What mistake I might be doing ?

I think it has to do something with 2s complements because 2s complement of 0000000 and 100000 are the numbers themselves.

What am I missing ?

Any help is highly appreciated.

Thanks.