Q - Is it possible to format a Samsung Android mobile phone and reload it with a Vivo operating system?

Yes, You Can 

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About Samsung

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Founded back in 1969 as Samsung Electric Industries, Suwon, South Korea-headquartered Samsung Electronics today makes everything from televisions to semiconductors. It released its first Android smartphone in 2009, and can be credited with the launch of the first Android tablet back in 2010. The company is among the biggest players in the smartphone market in the world. It has recently developed smartphones running Tizen OS, as an alternative to its Android-based smartphones.
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Samsung Smartphones Rom - BASIC ANDROID 

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About Vivo 

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Vivo Electronics Corp. is a phone brand based in Dongguan, Guangdong, China. It was founded in 2009. The company is another Chinese smartphone maker to enter India recently. It makes low-cost Android phones, and those in the mid-range segment of the market.
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Vivo Smartphones Rom - FUNTOUCH OS

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What is Custom Rom? 

The term ROM, which stands for Read Only Memory and really has very little to do with what a custom Android ROM actually is, can be confusing. A custom Android ROM refers to a phone’s firmware, based on Google’s Android platform. Android is open source and therefore any developer can edit the code, recompile it, and re-release for a wide variety of devices. Users can install ROMs to change a device’s appearance and behavior. ROMs are developed by the Android community, often times by a group of core developers who do this purely out of passion for modding. This means that most are completely free. Custom ROMs are available for phones, tablets, media players, smart watches and almost any type of device running Android.

When you buy your Android device, it comes with what we call a “stock ROM” or the “stock firmware”. This refers to the preinstalled operating system. This ROM usually has limited functionality as defined by the phone’s manufacturer. By flashing a custom ROM, you can unlock extra features and sometimes improve the performance.

What is Custom Recovery?

 A custom recovery is a third-party recovery environment. Flashing this recovery environment onto your device replaces the default, stock recovery environment with a third-party, customized recovery environment. This is a bit like flashing a custom ROM — but, instead of replacing your device’s Android operating system, it replaces the recovery environment.

Through Custom Recovery, You can easily replace your device’s Android operating system.

 CWM and TWRP are the two most popular custom recoveries, but other custom recoveries may be available for some devices.

Conclusion

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Last but not the least, you should have all the above knowledge before proceeding any task on your smartphone, because it may sometimes result a hard bricking or dead your smartphone, if any of the steps missed accidently.