iTunes keeps all your music, apps, podcasts, home videos, and anything else important to you. You can organize everything the way you want to and easily switch to any other device. You can use it to watch videos, or listen to your favorite music whenever and wherever you want.
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iOS users, especially those who own iPhones, often encounter strange errors 4013 and 4014, when they want to update their device to iOS 7 via iTunes. Simply put, it is a hardware problem. There are different solutions for this problem. With these 5 ways to fix iTunes error 4013, 4014 during iOS 7 Upgrade you will surely solve the issue, and you will be able to finish the update with no errors on the way.
5 ways to fix iTunes error 4013, 4014 during iOS 7 Upgrade

Source: cydiaos.com
Solution No.1: Latest version of iTunes
First, make sure that you have installed the latest version of iTunes on your laptop or desktop computer. When updating or restoring your iPhone, tons of issues can pop up just because you don’t have the latest version of iTunes, so this is a good place to start.
Solution No.2: USB port change
Change the USB port which connects iOS device and your computer, and use the original USB cable. This definitely is the simplest solution among these 5 ways to fix iTunes error 4013, 4014 during iOS 7 Upgrade, and sometimes, it definitely helps.
Solution No.3: Check for updates on your computer
Another thing you need to do that can be helpful is to see if there are any updates for your Mac or PC. If there are any updates, install them.
Solution No.4 Restart your iPhone and your computer
Press and hold the sleep/wake button, drag the slider, and power off your phone. When the phone is off, press and hold the sleep/wake button to turn it back on. Also, restart your Mac or PC and then try to upgrade to iOS 7.
Solution No.5: Clear the space on your iOS device
Clear out applications and delete some data you don’t need on your device (backup the files first) to free up some space on your iOS device. This sounds unrelated to this error, but it can help.