The HP Photosmart D110 series printer is fully compatible with both 32-bit and 64-bit Windows 7 as noted by the Windows 7 Compatibility Center on this page but a free download is required for full operation. Full report here.
You can get the updated drivers and software through the HP Support site by clicking here. Identify whether you have a D110a or D110b printer, then select whether you have Windows 7 32-bit or 64-bit.