There are several problems in your code. @MarkSolus have already pointed out that you access letters out-of-bounds because you are using i as index and i can be more than 1 when you do the memmove.
In this answer I'll address some of the other poroblems.
string size and termination
Strings in C needs a zero-termination. Therefore arrays must be 1 larger than the string you expect to store in the array. So
char nums[4]; // Can only hold a 3 char string
char letters[2]; // Can only hold a 1 char string
Most likely you want to increase both arrays by 1.
Further, your code never adds the zero-termination. So your strings are invalid.
You need code like:
nums[some_index] = '\0'; // Add zero-termination
Alternatively you can start by initializing the whole array to zero. Like:
char nums[5] = {0};
char letters[3] = {0};
Missing bounds checks
Your loop is a for-loop using strlen as stop-condition. Now what would happen if I gave the input "123456789BBBBBBBB" ? Well, the loop would go on and i would increment to values ..., 5, 6, 7, ... Then you would index the arrays with a value bigger than the array size, i.e. out-of-bounds access (which is real bad).
You need to make sure you never access the array out-of-bounds.
No format check
Now what if I gave an input without any digits, e.g. "HelloWorld" ? In this case nothin would be written to nums so it will be uninitialized when used in atoi(nums). Again - real bad.
Further, there should be a check to make sure that the non-digit input is one of B, kB, mB, or gB.
Performance
This is not that important but... using memmove for copy of a single character is slow. Just assign directly.
memmove(&nums[i], &input[i], 1); ---> nums[i] = input[i];
How to fix
There are many, many different ways to fix the code. Below is a simple solution. It's not the best way but it's done like this to keep the code simple:
#define DIGIT_LEN 4
#define FORMAT_LEN 2
int bitLength(char *input)
{
char nums[DIGIT_LEN + 1] = {0}; // Max allowed number is 9999
char letters[FORMAT_LEN + 1] = {0}; // Allow at max two non-digit chars
if (input == NULL) exit(1); // error - illegal input
if (!isdigit(input[0])) exit(1); // error - input must start with a digit
// parse digits (at max 4 digits)
int i = 0;
while(i < DIGITS && isdigit(input[i]))
{
nums[i] = input[i];
++i;
}
// parse memory format, i.e. rest of strin must be of of B, kB, mB, gB
if ((strcmp(&input[i], "B") != 0) &&
(strcmp(&input[i], "kB") != 0) &&
(strcmp(&input[i], "mB") != 0) &&
(strcmp(&input[i], "gB") != 0))
{
// error - illegal input
exit(1);
}
strcpy(letters, &input[i]);
// Now nums and letter are ready for further processing
...
...
}
}