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The player only enables HDCP on the HDMI output if HDCP is detected on the HDMI input.
Most game consoles enable HDCP on their HDMI output, though it may depend on the output mode or software being used.
SomeMacBookswill enable HDCP on the output if the destination device reports it supports HDCP, regardless of whether protected content is being displayed or not.
Some computer DVI graphics cards can support HDCP over DVI, as can some DVI AV devices like certain projectors and DVD players with DVI output, however, most DVI-HDMI conversion will lose HDCP.
Many early displays don't support HDCP over DVI and some early HDMI displays don't support HDCP over HDMI either. If it's not specifically mentioned, it probably isn't supported on the device.
There is an allowance in the DMCA for a HDCP-protected source device to allow SD (Standard Definition) analog output, but in practice this is rarely seen/used.
There are some instances where an HDCP-protected source can end up being output via analog on devices with both HDMI and analog outputs, but these should not be relied upon. This doesn't apply to current models without analog outputs. See Will-HDCP-content-display-over-an-analog-video-output?
HDCP 1.x and HDCP 2.x (available in HDMI 2.x) are separate entities. While HDMI 2.x devices are generally supposed to fall back to work with HDCP 1.x devices, it isn't always a smooth process.