Applied Course | Mock GATE | Test 1 | Question: 39

Question

A palindrome reads the same forwards and backwards. (For example, $10101$ and $1001$ are palindromes). Suppose you want a machine that takes a number with the four binary digits and outputs a $1$ only if the number is a palindrome.
You can build this with two XOR gates, one NOT gate, and which other extra kind of gate?

• A. AND
• B. OR
• C. XOR
• D. NOT

Answer 1

We want to check if A and D are equal, and B and C are equal; if so we have a palindrome.
A $XOR$ D will return $0$ if the inputs are same.
B $XOR$ C will return $0$ if the inputs are same.
Therefore we need to check if both of those expressions are $0$, that is NOT ((A XOR D) OR (B XOR C)).