"what would be the effect on the histogram if we set to zero the higher-order bit planes instead?"
Answers
Histogram: The representation of numerical data is distributed to determine the probability distribution of a continuous variable.
Consequence: If the histogram was set to zero, the image on the histogram will be sparse when compared with all other 8-bit plane case.
Reason: No component to represent the intermediate pixel values of 1,2,3,4, 5, 6,7 and 9,10,11,12,13,14,15. Only 0, 8 and 16 etc. This causes the peaks to increase in height and will result in reduced contrast.
Let us say we slice the LSB plane.
As a result, the last value of every pixel's in 8 bit will be 0.
Hence no ODD numbers can be there in the image.
Hence it will have 0 values corresponding to odd numbers.
Similarly, various combination of planes is possible to generated or discovered.
For a grey type imagery, when we set the lower-order bits at the point zero, the grey values of many of the pixels will be lowered to some extent.
As an example, the binary equivalent of 162 is 10100010.
If we set the last 4 bit planes at zero, the number will be 160.
However, the values of those pixels will not vary as these are already zeros at the respective positions.
The occurrences of 128, 128+64, 128+64+32, etc. will increase.
The histogram may slightly relocate to the left.