# How to find the reverse of a binary string with simple binary operators?

I was wondering is it possible to create a simple circuit that detects if an input (a binary string) is a palindrome?

So my approach is to feed the input to a circuit that reverses the input, ie if the input is 0111010, I need the output to be 0101110. Is this possible to achieve with only, and/or/xor/not and these simple operators in a generic way (on paper, not looking to implement a circuit with a predefined number of bits)?

Once I have this reversed output, I can use it with an "and" gate to compare to the original input and see if they match, but I'm stuck at the first part.

I appreciate your suggestions Thanks in advance

• What exactly is the input? How many "lines", clocked/"synchronous" or "asynchronous"? Sequential? (Reminds me of a basic example problem for one kind of automaton/machine.) – greybeard Mar 13 at 22:59

## 1 Answer

Yes, absolutely. Every boolean function can be implemented by a circuit. In this case, it suffices to XOR bits 1 and $$n$$; bits 2 and $$n-1$$; and so on; and then take the NOR of all of the outputs of these XOR gates.