In digital circuits, a decoder is a combinational logic circuit that converts an input code into one of several possible output lines. It takes an n-bit binary input and generates 2^n output lines, where each output corresponds to a unique combination of inputs. The outputs are typically represented in binary or one-hot format.
The primary purpose of a decoder is to enable the selection of specific output lines based on the input code. It is commonly used in various applications, such as memory addressing, data routing, control signal generation, and demultiplexing.
Let's take an example of a 3-to-8 line decoder, which is one of the most common types. It takes a 3-bit input (A, B, C) and generates 8 output lines (Y0 to Y7). The truth table for the 3-to-8 decoder is as follows:
A B C Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7
0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 0 0 0 0 0 0
0 1 0 0 0 1 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 0 1 0 0
1 1 0 0 0 0 0 0 0 1 0
1 1 1 0 0 0 0 0 0 0 1
For example, if the input code is "011," the third output line (Y2) will be active (i.e., "1"), and all other output lines will be inactive (i.e., "0").
Decoders are often used in combination with encoders, multiplexers, and demultiplexers to create complex digital circuits for various applications in computer systems, memory addressing, communication systems, and more. Their efficient implementation is crucial for the proper functioning of digital systems.