Can I update the iOS on a MacBook Air 11.6 inch?

For the Record - iOs is for iPhone and iPads. MacOS is for computers.

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. Make sure to use Only Safari to commence the download as Others may not work. Safari will open a redirect and open the Apple Store where you can commence the download. If an error message appears, that is probably because one is using another Browser.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Make a Time Machine Backup Before attempting. Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina & Big Sur support 64 bit and there is no workaround.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation

Back up your data, check your applications for compatibility, and depending on which MacBook Air model you have, click on High Sierra, Mojave, Catalina, or Big Sur.

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iOS is for iPhone, macOS is for computers

2011 -> Up to macOS High Sierra

2012 -> Up to macOS Catalina

2013/2014/2015 -> Up to macOS Big Sur