Since we are restricted to (0,1), a binary system can be used to simulate the inputs. For example, a --> 00, b --> 01, c --> 10. Then, input abc will be repe5rsented by 000110. Also, the original turing machine has the input length of n. This indicates the new turing machine will have log(n). But there are 3 steps that the turing machine will take: read, write, and move right or left. Each of these will take log(n) time. Then, the slow down will be 3*log(n).

For simulating the larger inputs by introducing new symbols with combination of {0,1}. E.g A -> 00, B ->01, C -> 10, d -> 11. If the original machine as an input length of n, then new machine created has log(n) as an input. And the Turing Machine will have to transfer into a state of that input. The new machine has to perform the flowing instructions read, write, moving left and right. We know that all instructions need log(n). So the expected slowdown is 3log(n).

Simulating a machine with a larger input or tape alphabet, we need to limit the input alphabet to the {0, 1}. We need to create a map of our two symbols, from the alphabet, such as 00, 01, 10, or 11. The original TM has input length of n. The modified or augmented machine will have input of log(n) for reading, writing.

We will use binary to simulate the larger inputs Mapping : A -> 00 , B -> 01 , C -> 10 The tape reads 2 of the {0, 1} symbols to map to the original alphabet. If the original machine as an input length of n, then new machine created has log(n) as an input.The new machine has to perform the flowing instructions read, write, moving left and right. We know that all instructions need log(n). So the expected slowdown is 3log(n).

We will encode the alphabet in a way similar to grey code where A -> 00, B->01, and C->10. If the original machine as an input length of n, then the new machine will have the input length of log(n). since the turing machine needs to read (log(k)), write (log(k)) and move left and right (log(k)), the total amount of time to do such is 3log(k).

We can simulate larger inputs by using a binary system. Eg : 00 -> A, 01 -> B , 10-> C and so on. If the original TM has n inputs, the new machine created has log(n) inputs. The new machine performs read, write , moving left and right. The expected slowdown is 3log(n)

In order to simulate a machine with a larger input or tape alphabet, we can limit the input alphabet to {0, 1}.

intput : 0, 1

tape: 0, 1 ,□

so if we have a large input, we can have a different input such as 00, 01, 10, 11, and in TM, we can write new inputs and read them to match the tape. The machine will have an input of log(n) for reading, writing and moving right or left. where n= length of inputs.