The highest bit set in a particular column does not represent a piece. There will always be at least 1 bit set in each column, and the set bits beneath that dummy bit are the pieces of a particular colour. Bits not set beneath the highest set bit represent pieces of the other colour. You need an extra row to have room for the dummy bit.
Empty board 1111111 After first move, middle column (player who goes first represented by a 1) 0001000 1111111 Next player plays on top of that 0001000 0000000 1111111 If they had played to the right instead of on top, the board would be 0001100 1111011 etc.