The transition was tricky: assembly language programmers, including IBM's own operating systems architects and developers, had been using the spare byte at the top of addresses for flags for almost twenty years. IBM chose to provide two forms of addressing to minimize the pain: if the most significant bit (bit 0) of a 32-bit address was on, the next 31 bits were interpreted as the virtual address. If the most significant bit was off, then only the lower 24 bits were treated as the virtual address (just as with pre-XA systems). Thus programs could continue using the seven low-order bits of the top byte for other purposes as long as they left the top bit off. The only programs requiring modification were those that set the top (leftmost) bit of a word containing an address. This also affected address comparisons: The leftmost bit of a word is also interpreted as a sign-bit in 2's complement arithmetic, indicating a negative number if bit 0 is on. Programs that use signed arithmetic comparison instructions could get reversed results. Two equivalent addresses could be compared as non-equal if one of them had the sign bit turned on even if the remaining bits were identical. Most of this was invisible to programmers using high-level languages like COBOL or FORTRAN, and IBM aided the transition with dual mode hardware for a period of time.