Bitwise nuggets: clear the first k most significant bits
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# Bitwise nuggets: clear the first k most significant bits

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:

```1 2 3 4 5 pos: 10 0 v v 2019 = 11111100011 ^ ^ MSB LSB ```

Clearing the `k` MSBs in a number would mean zero-ing 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:

```1 2 3 4 5 6 7 8 9 10 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 left-shifting 1 by the difference between the total number of bits and `k`, then subtracting 1 (to get all ones). The mask is applied by AND-ing 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:

```1 2 3 4 5 6 // 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):

```1 2 3 4 5 6 7 8 9 10 11 12 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.