Is there adapters for component cables to HDMI cables?

Answer 1

Analog component signals are completely different to digital HDMI. There is no simple adaptor cable because the analog signals require processing to convert to digital. There are converter units that will perform the processing as dedicated converters but it may also be possible to use other equipment such as DVD recorders. Many have analog inputs with an HDMI output and it is often possible to route a signal straight through the unit.

Converting from HDMI to analog component is rather harder. In fact it is not possible to do it using authorized hardware. HDMI uses a copy protection system known as HDCP which encodes the signal. Converting that HDMI signal to analog removes the copy protection and no legitimate devices are available that will remove copy protection. There are some exceptions to the HDCP system, mostly for non commercial content but in these cases, there are normally easier ways to obtain analog copies.

There are a handful of unauthorized converters but be warned that even if they operate now, they can be disabled if they are known to be unlicensed devices.

I don't know about the truthfulness or accuracy of the above information , but a PS3 has an HDMI input and does have optional cables that have a component connection at the HDTV side and a HDMI connection on the other side. They ran about $30 and are designed to connect a PS3 to a HDTV with component cables and may work for your connection