If you perform all your calculations based on x and y, (Where Y is a vertical coordinate from 0-7, and X is horizontal 0-7), the position in your 1D bit board will be y*8 + x From there, its a simple mathematical translation, using the relationship between X and Y eg, for a translation which rotates 90 degrees right, the bit at the virtual coords [ X, Y ] translates directly to [ 7-Y, X ] a left-r