1. (a) A palindrome is a string that is the same backwards and forwards. (12 points) i. How many binary palindromes are there of length 2n? ii. How many bits would the most efficient encoding of such strings use? (in terms of n.) iii. Develop your own encoding/decoding algorithm where the code uses this number of bits. (Please give a brief description of how it works on an arbitrary input.) iv. Use your encoding to encode the following strings: . 0011001100 . 0110110110 010010 v. Use your decoding to decode the following strings: (put "not decodable" if you can't decode the string.) 110 . 101 000 1. (a) A palindrome is a string that is the same backwards and forwards. (12 points) i. How many binary palindromes are there of length 2n? ii. How many bits would the most efficient encoding of such strings use? (in terms of n.) iii. Develop your own encoding/decoding algorithm where the code uses this number of bits. (Please give a brief description of how it works on an arbitrary input.) iv. Use your encoding to encode the following strings: . 0011001100 . 0110110110 010010 v. Use your decoding to decode the following strings: (put "not decodable" if you can't decode the string.) 110 . 101 000