Final answer:
The device that converts digital signals from a cable into analog signals that older TV sets can interpret is a digital-to-analog converter or a set-top box. This device is integral for older TVs with cathode ray tube technology, which cannot directly interpret digital signals.
Step-by-step explanation:
The device that converts the digital signals carried by the cable into analog signals compatible with the TV set is known as a digital-to-analog converter (DAC) or a set-top box (STB). This device is essential for converting digital data transmitted in the form of binary ones and zeros into a format that can be displayed on a traditional analog television. The function of the DAC or set-top box is to take the digital signal that comes from cable, satellite, or a digital broadcast, and convert it into an analog signal that older TVs can display. In the case of more modern television sets, including flat screens with HD capability, they can process digital signals directly without the need for a separate conversion.
With regard to older TV sets, such as those utilizing cathode ray tube (CRT) technology, a digital-to-analog converter box was required to display digital broadcasts. As more consumers transitioned to flat-screen TVs, the necessity for external DACs diminished since newer TVs came equipped with built-in digital tuners. It's important to note that the transition from analog to digital broadcasting was part of a movement to improve the quality of television transmission, leading to developments such as high-definition (HD) broadcasting.