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Editorial Team
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Asked: 2026-05-26T23:14:08+00:00

How to exchange bits of given integer number {p, p+1, …, p+k-1} with {q,

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How to exchange bits of given integer number {p, p+1, ..., p+k-1} with {q, q+1, ..., q+k-1} in case where we have an overlap of both bits intervals;
p and q are bit’s positions:
p != q; k > 1.

Example:

p = 5;
q = 8;
k = 6;
16-bits decimal number 30 000 in binary representation:
01110101 00110000
================before exchange============
     101 001
  110101
================after exchange==============
     110 101
  101001
============================================

How to decide for bit’s positions 8, 9 and 10, which bits to put – 110 or 001?

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1 Answer

  1. Editorial Team

    The algorithm, if allowing overlaps, must be a lossy one.

    From your example:

    01110101 00110000
     |     |
     101 001
  |    |
  110101

    If you swap them, the values are:

    01110101 00110000
     |     |
     110 101
     *** - Mismatch!
  |    |
  101001
     *** - Mismatch!

    No matter what, if you allow an overlap, you cannot guarantee you can get the same original values out after doing the swap.

    Two ways to deal with this problem:

    • Document that your function is lossy, and that you cannot guarantee that you will be able to extract the swapped bits back out.
      I don’t like this idea, because I don’t know what I’d use such an algorithm for
    • Throw an exception if an overlap is fed into the algorithm, and write your program that uses this algorithm in such a way that it doesn’t generate overlaps.
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