Q5: Implement PALINDROME circuit

Q- Draw the circuit to check a PALINDROME number of even bits.

Ans: Palindrome number (in bits) is the number which is same whether seen from the first and the last bit. E.g. 1001, 0110, 0000, 1111 in 4 bits

So to check this we need to have same value of bit at 1^st bit and 4^th bit, 2^nd and 3^rd bit position for a 4-bit number. For a 6-bit number we need to have same bits at 1^st and 6^th bit, 2^nd and 5^th bit, 3^rd and 4^th bit positions.

Hence to check whether bits in different pairs have same value we need to have XNOR gate and then AND them to see whether all pairs satisfy the condition.

So we have the general circuit as next:

We can verify this for a 4-bit number as done next.

 So K-map for that is as

And hence we see that we need to XNOR the corresponding bits and then take AND of all outputs of XNORs