What is the purpose of a decoder in digital circuits?

A decoder plays a critical role in digital circuits by converting binary input into a unique output line. When given an n-bit binary input, a decoder generates 2^n output lines. Each output corresponds to one combination of the input binary values, thus ensuring that only one output line is activated at a time based on the input. This property is essential for tasks such as selecting among multiple devices, enabling specific circuits, and facilitating communication between components within a digital system.

For instance, in a simple 2-to-4 decoder, if the binary input is 01, the output line corresponding to the decimal value 1 (which is the second output line) will be activated, while all others remain inactive. This capability is fundamental in a variety of applications, including memory address decoding and data routing in multiplexers, making the decoder an integral component in binary logic systems.