Even though most people have more DVDs than Blu-rays and there are more standard-definition (SD) channels than high-definition (HD) on all cable/satellite providers, it's highly unlikely most people send their televisions standard-definition signals.
Nearly all current DVD players, and all Blu-ray players, convert the SD from a DVD to HD. Nearly all cable/satellite boxes upconvert the SD channels to HD. Since this upconversion happens before the signal is sent to the TV, most properly hooked-up HDTVs today only ever receive HD signals.
The only readily available SD source is Nintendo's Wii.
There is a practical thought behind this esoteric question. If no SD is ever sent to a television, is the standard-def processing of a TV, and the associated SD inputs, irrelevant?
What do you think? Do you still have, and regularly use, any SD sources?
It also might be good to check that you're actually watching HD on your HDTV.