Here we discuss how to clear the first k
most significant bits (MSB) in an integer. This is a more intuitive variation of the clear MSB up to a given position problem that we have seen earlier.
What does that even mean? Well, in a number, bits are numbered starting from 0, where the bit at position 0 is the least significant bit (or LSB for short). Take the number 2019 for instance; its LSB (at position 0) is 1 and its MSB (at position 10) is also 1:
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pos: 10 0
v v
2019 = 11111100011
^ ^
MSB LSB
Clearing the k
MSBs in a number would mean zeroing them out while leaving the LSBs untouched. For example, if we were to clear the first 3 MSBs in number 2019 up, we would get 227:
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k: 3
v
2019 = 11111100011

v
clear the 3 MSBs
k: 3
v
227 = 00011100011
The idea is to apply a mask to the integer, where the mask is all zeroes for the k
most significant bits, i.e. the bits we want to clear. The remaining mask is all ones. We obtain the mask by leftshifting 1 by the difference between the total number of bits and k
, then subtracting 1 (to get all ones). The mask is applied by ANDing it with the number. It has the effect of preserving the LSBs and of clearing (zeroing) the first k
MSBs.
We first need count_total_bits()
, a helper function to count the total number of bits in a number. Using this function, we can now clear the k
most significant bits as follows:
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// Clears the first `k` most significant bits in `number`.
int clear_most_significant_bits(int number, unsigned int k)
{
unsigned int n_bits = count_total_bits(number);
return number & ((1 << (n_bits  k))  1);
}
Here is what becomes of number 2019 when we clear its MSBs up to positions 0 through 11 (recall that the MSB of 2019 is at position 10):
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clear_msb(2019, 0) = 2019 = 11111100011
clear_msb(2019, 1) = 995 = 01111100011
clear_msb(2019, 2) = 483 = 00111100011
clear_msb(2019, 3) = 227 = 00011100011
clear_msb(2019, 4) = 99 = 00001100011
clear_msb(2019, 5) = 35 = 00000100011
clear_msb(2019, 6) = 3 = 00000000011
clear_msb(2019, 7) = 3 = 00000000011
clear_msb(2019, 8) = 3 = 00000000011
clear_msb(2019, 9) = 3 = 00000000011
clear_msb(2019, 10) = 1 = 00000000001
clear_msb(2019, 11) = 0 = 00000000000
Want to see more bitwise logic? There’s a whole repository on my GitHub on bit fiddling.
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