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How can I change the 8bit rgb images into 12bit rgb image

I have mapped and sampled each channel to 12 bit.

Example: 8 bit image- R[0-255], G[0-255], B[0-255] mapped to 12 bit image - R[0-4095], G[0-4095], B[0-4095]

----> formula used: (8 bit image intensity * 4095) / 255

12 bit image = (8 bit image intensity * 4095) / 255

is this the right way to convert into 12 bit? if no please suggest the possible way to do it