Hello
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I understand you are having troubles with installing your Photosmart B109 on your new Windows 8 system. I do have some suggestions for you to hopefully help you.
Try installing the printer by using HP Printer Install Wizard for Windows which will search for the correct driver and install it for you. This method may work.
Also, ensure you complete your Windows Updates, select even the optional ones: Windows Update - Do I need to check for updates?
Please let me know the outcome, if you need further help, I will investigate this issue further for you.
Thanks,