given to binary numbers x an x+2 without truth table ,adders or subrtactors output x+1?

i tried many examples for even numbers there is a goo logic but for odd numbers its very hard

 

In the design of adders there is the concept of a logic function for the carry called generate/propagate/kill. Starting with the least significant digit of x, if there is a zero, the result for bit 0 is a 1 and the kill signal says that's it you're done. As long as generate/propagate/kill says generate/propagate you move on to the next most significant bit, and keep going until you get a kill.

http://www.cerc.utexas.edu/~jaa/vlsi/lectures/8-1.pdf

Now you should be able to look at x and x+2 and figure out which bits don't change. Now all you have to do is develop a theorem about x+1.

 

given to binary numbers x an x+2 without truth table ,adders or subrtactors output x+1?

i tried many examples for even numbers there is a goo logic but for odd numbers its very hard

What ARE you allowed to us? Just basic gates? Can you use 2:1 Muxes?

Look at the behavior of the last bit and the rest of the bits separately.