There are some patents out there that are very basic and most trivial. Can I patent and/or manufacture a product that builds on a patented product (I don't own the "basic" patent)

For example, there are a lot of patented power supply strips that turn off devices based on a "master" device's power draw (your computer peripherals switch off if the "master" computer goes into standby).

I want to build "smart remote" power supply strips that not only does the above but also can be configured over WiFi and household remote control (so that you can turn your power-hungry fax machine on/off remotely or while watching TV)

If I build my version of "smart remote" power supply strips am I infringing on the existing patented power supply strips?

Assume there are some patents out there that seem to be fundamental and almost trivial. 

Can I patent and/or manufacture a product that builds on a patented product (I don't own the "basic" patent)

For example, there are a lot of patented power supply strips that turn off devices based on a "master" device's power draw (your computer peripherals switch off if the "master" computer goes into standby).

I want to build "smart remote" power supply strips that not only does the above but also can be configured over WiFi and household remote control (so that you can turn your power-hungry fax machine on/off remotely or while watching TV)

If I build my version of "smart remote" power supply strips am I infringing on the existing patented power supply strips?