Final answer:
The device designed to convert digital signals into analog signals for display on traditional TVs is a Set-top box (STB). DTAs also work for this purpose but with limited features, while DVRs record TV programs and DVDs are a storage format.
Step-by-step explanation:
The device that converts digital signals carried by the cable into analog signals that are compatible with a traditional TV set is a Set-top box (STB). A set-top box decodes the digital signal received from the cable and converts it into an analog format that a standard TV can display. Digital Terminal Adapters (DTAs) can also serve a similar purpose for basic channel conversion, but they are more simplified versions of set-top boxes intended for allowing analog TVs to receive digital broadcasts.
For the other options, Digital video recorders (DVRs) are primarily used for recording television programs digitally, Digital versatile discs (DVDs) are a type of optical disc storage format for video, audio, and other data, and DTAs are mainly for digital-to-analog conversion but with less functionality compared to a full-fledged STB.