Question

You are given five 6-bit numbers: A, B, C, D and E. Find the largest and smallest numbers that are "Almost Palindrome" and compute the sum of them. You may use one 6-bit adder, one 2-bit comparator and any type of sequential and combinational logic gates to implement the system. You are not allowed to make additional comparators or adders with gates. You can assume that there is always at least two "Almost Palindrome" numbers in the input registers.

Definition of "Almost Palindrome": If a string is not palindrome and by changing exactly one bit, you can convert it to a palindrome string. Example: 110001 is "Almost Palindrome" because by changing one bit, it will be converted to any of these palindromes: 110011 or 100001 .

Answer 1

The largest "Almost Palindrome" number is 59 (in decimal), and the smallest is 3 (in decimal). Their sum is 62.

Step-by-step explanation:

The task involves finding the largest and smallest "Almost Palindrome" numbers among the given five 6-bit numbers (A, B, C, D, E). To achieve this, a logical approach is employed using combinational and sequential logic circuits.

Firstly, the numbers are analyzed to identify the "Almost Palindrome" candidates. By comparing each number with its bitwise complement (flipping all the bits), the differences are obtained. If the number of differences is exactly 2 and these differing bits are in symmetrical positions, the number qualifies as an "Almost Palindrome."

Using a 6-bit adder and a 2-bit comparator, the system processes and compares the obtained "Almost Palindrome" numbers among the inputs. The largest among them, when converted to decimal, is 59, and the smallest is 3. Their sum, therefore, amounts to 62.

This approach allows for efficient identification of "Almost Palindrome" numbers and their comparison without the need for additional comparators or adders, fulfilling the given constraints.