I need to write a function called compress(S) that takes a binary string S of length less than or equal to 64 as input and returns another binary string as output. The output binary string should be a run-length encoding of the input string.

Run-length coding represents an image by a sequence (called a "run-length sequence") of 8-bit bytes:

The first bit of each byte represents the bit that will appear next in the image, either 0 or 1. The final seven bits contain the number in binary of those bits that appear consecutively at the current location in the image.

>>>compress( 64*'0' )
'01000000'
>>> compress( '11111' )
'10000101'
>>> Stripes = '0'*16 + '1'*16 + '0'*16 + '1'*16
>>> compress(Stripes)
'00010000100100000001000010010000'

First Run Length Encoding, define it as-

def rle(input_string):
            """ takes input as string and checks repeating bit
                return repeating bit with their counts.
            """
            count = 1
            prev = ''
            lst = []
            for character in input_string:
                if character != prev:
                    if prev:
                        entry = (prev,count)
                        lst.append(entry)
                        #print lst
                    count = 1
                    prev = character
                else:
                    count += 1
            else:
                entry = (character,count)
                lst.append(entry)

            return lst

Produce list of tuples.

Input: print rle('1111010')

Output: [('1', 4), ('0', 1), ('1', 1), ('0', 1)]

 ----------------------------------

Now use this list to make dictionary with binary conversion of repeating counts and format it to 7 bits long. And finally add the respective key and values of the dict so that total digit remain 8 bits.

def new_dict(S):
            """ input of rle(S) i.e., tuples of bit and repeating counts
                output dict as bit as key and value as counts with binary conversion.
            """  

            dict=rle(S)
            new_dict = []
            temp = []
            for k,v in dict:
                temp = k + "%07d" % int(bin(v)[2:])
                new_dict.append(temp)
            return new_dict

input: print new_dict('1111010')

output: ['10000100', '00000001', '10000001', '00000001']

Now compress this binary string with the compress(S) function.

        def compress(S):
            """ takes a binary string S of length less than or equal to 64 as input and returns another binary string as output. 
            """
            l = new_dict(S)
            return''.join(str(elem) for elem in l)

print compress('1111010')
print compress( 64*'0' )