convert rgb image to binary in pillow

from PIL import Image 
image_file = Image.open("cat-tied-icon.png") # open colour image
image_file = image_file.convert('1') # convert image to black and white
image_file.save('/tmp/result.png')

from PIL import Image

col = Image.open("cat-tied-icon.png")
gray = col.convert('1')
bw.save("result_bw.png")