Suppose we want to invert the n least significant bits in a number. For example:
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2019 = 11111100011
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2028 = 11111101100
If we invert the least significant 4 bits in the number 2019, we obtain 2028.
When we hear invert, we automatically think of XOR:
0 XOR 0 = 00 XOR 1 = 11 XOR 0 = 11 XOR 1 = 0
We therefore need to XOR the input number with a mask of n bits that are all 1…1. To obtain this mask, we can left-shift 1 for n positions, then we subtract 1. Following our previous example:
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2019 : 11111100011
mask = 1 << 4 : 10000
mask -= 1 : 01111
2019 ^ mask : 11111101100 = 2028
Here is how this operation may be implemented in C:
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// Inverts the `n_bits` least significant bits in `number`
// and returns the resulting number.
int invert_n_lsb(int number, int n_bits)
{
return number ^ ((1 << n_bits) - 1);
}
Want to see more bitwise logic? There’s a whole repository on my GitHub on bit fiddling.
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