If the image you saw is like this one, D0-D7 imply bit positions in the status register, called F (for flags) when part of the AF register pair. The Ds are misleading because they imply some (nonexistent) relationship to the D register or the data pins (which are multiplexed with the address lines and are actually called AD0-AD7).
Describing bit positions for the status flags doesn't mean much of anything for most people because the only instructions that operate on F deal with a single bit at a time (conditional jumps, conditional subroutine calls and the instructions that set and clear the carry flag). The only way to operate on the flags as a whole would be to transfer them to or from another register by way of the stack.