Digital signals are like images made from only two colors: full black and full white. You can make out such an image even if it is very noisy. So you can send a signal at a level that would be extremely fuzzy on an old analog TV, but the digital circuitry can still pick out the data reliably.
Instead of an actual image, a string of ones and zeroes (black and white color) representing an image is transmitted, and as long as the TV can make out each of them, it can recreate a pristine image.
This is a simplification, but it illustrates the basic premise.
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