The decoder in computer architecture is essential for translating encoded data into a format that the system can comprehend and process.

To elaborate, a decoder is a critical component within a computer system’s architecture. It is a combinational circuit that transforms binary information from $n$ input lines into a maximum of $2^n$ unique output lines. Among these outputs, one will be active, based on the values present on the input lines. In essence, a decoder performs the inverse operation of an encoder.

The primary function of a decoder is to interpret and convert coded data into a usable format for other components of the computer. For instance, within a CPU, the instruction decoder receives encoded instructions from memory and translates them into a series of control signals, which orchestrate operations on the processor’s data.

Decoders are also instrumental in memory addressing, enabling access to a large memory space using fewer address lines. For example, a $2$-to-$4$ line binary decoder can accept an input of two binary digits and decode it into one of four outputs, each corresponding to a distinct memory location.

Furthermore, decoders are pivotal in the implementation of multiplexers and demultiplexers, which facilitate data routing among various components of a computer system. A multiplexer employs a decoder to select one out of many inputs, directing the chosen input to a single output line. Conversely, a demultiplexer uses a decoder to take a single input line and route it to one of several output lines.

In summary, the decoder is a vital element in computer architecture, playing a crucial role in data interpretation, memory addressing, and data routing. Its primary function is to translate encoded data into a format that can be understood and processed by the computer system, thereby facilitating efficient and effective communication between different components of the computer.