A lot of TVs don't actually pick up the correct resolution in Windows when using HDMI. Some of them have to be set to 1920x1080 in the screen resolution control panel and in some cases with discrete graphics cards, you need to adjust the overscan options to make the image scale up to all the four edges of the panel.
Otherwise, run the TV in 1024x768. Works every time, zero incompatibility issues, just make sure that your displays are extended and not mirrored.
To reduce resolution in Windows 7: Right-click Desktop > Screen Resolution > Click on the Multiple Displays option to set up the second display as an extended one. Then use the Resolution drop-down list to set it to the correct setting.
If you'd also like to output sound over HDMI for watching a movie or series you'll need to use a third-party player like
VLC and dig into the system preferences. In audio you need to change the default playing device to Direct X Audio Output and set the device to the one using the HDMI cable.
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