Ballpark figure for a HDMI to VGA decoder is around 200 mA at 5 volts. That's a watt. For such a small device, you're going to expect that to make it fairly warm.

For example, your TV likely has HDMI 1.4 connections, which max out at 3,820x2,160-pixel resolution at 30 frames per second. If you've gotten a new 4K monitor, you're limited to 30fps.

Adapters are available to connect VGA monitors to laptops that have HDMI or DisplayPort. NPD In-Stat is forecasting shipments of devices with DVI, HDMI and DisplayPort to pass 2 billion by 2015.