Cant really put my finger on what you are doing wrong, but the code seems to be more complex then it has to be.

Instead of doing the read operations, let base64 module handle it for you

import base64
with open('noaa19-161015.png', 'rb') as fp, open('test.b64', 'w') as fp2:
    base64.encode(fp, fp2)

with open('test.b64', 'rb') as fp, open('test.png', 'wb') as fp2:
    base64.decode(fp, fp2)

Also noticed that you are trying to encode a already encoded string look at the row base64.b64encode(string)

I'm not sure I understand your question. I assume you are doing something along the lines of:

import base64

with open("yourfile.ext", "rb") as image_file:
    encoded_string = base64.b64encode(image_file.read())

You have to open the file first of course, and read its contents - you cannot simply pass the path to the encode function.

Edit: Ok, here is an update after you have edited your original question.

First of all, remember to use raw strings (prefix the string with 'r') when using path delimiters on Windows, to prevent accidentally hitting an escape character. Second, PIL's Image.open either accepts a filename, or a file-like (that is, the object has to provide read, seek and tell methods).

That being said, you can use cStringIO to create such an object from a memory buffer:

import cStringIO
import PIL.Image

# assume data contains your decoded image
file_like = cStringIO.StringIO(data)

img = PIL.Image.open(file_like)
img.show()

This should do it in Python:

import base64

binary_fc       = open(filepath, 'rb').read()  # fc aka file_content
base64_utf8_str = base64.b64encode(binary_fc).decode('utf-8')

ext     = filepath.split('.')[-1]
dataurl = f'data:image/{ext};base64,{base64_utf8_str}'

Thanks to @cnst comment, we need the prefix data:image/{ext};base64,

Thanks to @ramazanpolat answer, we need the decode('utf-8')