I had the same error:
simplyphp posted the solution that worked for me here: http://community.us.playstation.com/t5/PlayStation
Following his instructions there resolved my issue, I was using the 308MB update and not the full version he links to.
I'll paste his post here:
"The problem is you are trying to do option 3, Update System Software.
If you removed your 500GB drive, like I did which I replaced with a 1.5TB 5400RPM 2.5" drive, then you need to do option #7.
Also, you need to download the 859MB full 1.5 file from the playstation website:
Put it on your flash drive in this structure:
D:\PS4\UPDATE\PS4UPDATE.PUP (where D: is your flash drive's drive letter)
Then plug the flash drive into PS4 with it powered off, plug your USB cord into your DualShock 4 controller. Power the system into safe mode by pressing and holding for 7+ seconds until you hear the second beep. Choose option 7, choose YES to reinitiliaze. It will copy the file off the flash drive onto the hard drive, reboot the PS4, then ask you to proceed with the installation.
Hope this helps!"
I had the same error with a stock HDD and turns out it was bad so I had to send it in for repair. I'm thinking the solution works people who put in new HDD's but for people who it just errors out on a stock/old HDD then it's an error code for faulty HDD and firmware won't install.
Put the downloaded file on your flash drive in this structure:
D:\PS4\UPDATE\PS4UPDATE.PUP (where D: is your flash drive’s drive letter)
Turn off your PS4. Make sure that the power indicator is not lit. If the power indicator is lit up in orange, touch the power button on the console for at least 7 seconds (until the system beeps a second time).
Change the HDD, connect the USB to the PS4 and turn it on (keep the power button pressed for 7 buttons). The console will boot up in Safe Mode.
Select Initialize and update software (last option on the Safe Mode screen) and follow the instructions to complete the update.
And that’s it!
What a pain in the neck! I spent the last hour trying to get this to work. With downloading the 800MB + sized file, then putting it on my usb drive, then initiating the update #7 option, then it always failing at some point just before the install takes place with various error messages. I tried 2 other USB sticks, and redownloading the file, and then right when I was so frustrated I was about to call tech support the darn thing worked!
Once the install took, it was a piece of cake. It was very strange as to why it was such a friggin headache. Maybe there is somehting loose, or my new USB device is tempremental, I dunno.