Cell phone signals are repeatedly blocked by electromagnetic radiation from the sun. However, GPS devices, which receive a much fainter signal from satellites, continue to operate. For that matter, television broadcasting, which relies on satellite relays, continues until the end of the film. See more...
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Continuity: When John is decoding the numbers for the first time, he uses a whiteboard. On the whiteboard are, presumably, spelling words for Caleb. He erases some of these to make room for the numbers. In the various shots of this scene, words disappear and reappear continuously, often written slightly different.