This one originally came up for me in Oodle Texture's BC7 decoder. In the BC7 format, each pixel within a 4x4 block can choose from a limited set of between 4 to 16 colors (ignoring some caveats like the dual-index modes that don't matter here) and consequently between 2 and 4 bits per pixel are…

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Ryg blog

A method for inserting a 0 bit in the middle of a value, inspired by Oodle Texture's BC7 decoder, is discussed. The post details both a standard and a more optimized approach for this operation. It also includes an analogous method for removing a 0 bit from the middle of a value.

Inserting a 0 bit in the middle of a value