A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines. If the n-bit decoded information has unused or don’t care combinations, the decoder output will have less than 2n outputs.
This article explains n-to-m line decoders where m <= 2n. They generate 2n or less minterms of n input variables.
Consider an example where three inputs are decoded into eight outputs and each represents one of the minterms of the 3-input variables. The three inverters provide the compliment of the inputs, and each one of the eight AND gates generates one of the minterms.
The following truth table shows the input-output relationships for the operation of the decoder.
| Inputs | Outputs | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| X | Y | Z | D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7 |
| 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 |
In the above truth table, the output variables are mutually exclusive because only one output can be equal to 1 at any one time. In the first row of the table D0 is 1, in the second row D1 is 1 and so on.
An application of this decoder is binary-to-octal conversion. The input variables can represent a binary number, and the outputs will then represent the eight digits in the octal number system. However 3-to-8 line decoder can be used for decoding any 3-bit code to provide eight outputs, one for each element of the code.
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