Simple YCrCb to Grayscale conversion

Hello! I have a video decoder outputting Composite Video Data in the YCrCb 4 : 2 : 2 scheme.I was wondering if it would be possible to get a "fairly working" translation from the YCrCb data to grayscale in the 24-bit RGB domain by setting R = G = B = Y(The Luma Component) of the pixel? I realize that the question is very subjective, but what I mean by fairly working is something similar to the picture here : Sample Image

The Y values for the input range from 16 to 235.