Final answer:
The network interface device that converts between framing formats on a digital circuit is the CSU/DSU.
Step-by-step explanation:
The type of network interface device (NID) that includes circuitry to perform functions such as converting between framing formats on a digital circuit is a CSU/DSU (Channel Service Unit/Data Service Unit). A modem can convert digital signals to analog and vice versa, but it doesn't usually convert framing formats. A router forwards data packets between computer networks, and a switch connects devices within a single network and filters and forwards packets to different devices in the same network.