Analog to digital RCA conversion

I'm working on an arduino powered project now that is a giant audio/video switch for my collection of old video game systems. It's got 16 inputs switched between 2 outputs and its great for having friends over and playing lots of video games. All the outputs are those yellow/red/white RCA cables.

Unfortunately, I have it hooked up to two CRT tvs with a big HDTV in between. It's kinda awesome but mostly inconvenient. After I finish the switch box project I want to look into designing something that will basically split screen the two outputs of the switch box on the HDTV so I can ditch the CRTs.

Does anyone know of any chips or boards that will take an RCA signal and convert it to a digital signal that could be processed by a computer? Preferably without upscaling the signal to 1080p

I doubt this project will be as dependent on an Arduino as the switch box but I'm sure one could handle the buttons on the box or something.