can I install cement backer board over plank subfloor
My experience is no, too much bounce. Either install 1/2-3/4" t&amp;g ply over it (glued &amp; nailed), or cut it out and install new t&amp;g 3/4 subfloor, glued and nailed.

Also consider your floor joist width and span. In this question, that's undetermined.

In either case, then you can install 1/2" cement board.