## What is a Binary Decoder?

A binary decoder (sometimes referred to as just a “decoder”) is a combinational logic circuit that converts binary information from the n coded inputs to a maximum of 2^{n} unique outputs. Binary decoders are used in an extensive number of applications—notably data multiplexing and data demultiplexing and seven segment displays.

But that definition can be a little confusing… so what is a binary decoder actually used for?

Well, a binary decoder converts a **definite sequence of input bits into a specific pattern**.

The specifics of this pattern will depend on what you’re using the binary decoder for.

To help explain this, let’s look at an example problem.

Figure 1 below shows a binary decoder with one enable pin and 3 input lines, which results in 8 lines at its output (as 2^{3} = 8).

The output sequence of a binary decoder for a particular input pattern is realized using its truth table (note: a truth table is a mathematical table that lists the output of a particular digital logic circuit for all the possible combinations of its inputs).

Table I shows the truth table for the decoder of Figure 1, which shows that when the enable is low, all the output lines are low, no matter what the input sequence is.

This indicates the OFF state of the decoder which can also be considered to be its reset state.

Thus one has to drive high on the enable pin to realize the functionality of the decoder.

Table I shows that for the input sequence I_{2}I_{1}I_{0} = 000, the output pin O_{0} of the decoder is high while all other bits (O_{7} down to O_{1}) remain low.

Likewise, for the input sequence of 001, only O_{1} is high. Similar observation shows that only one output line is high for any given input bit pattern i.e.

O_{2} is high for 010, O_{3} is high for 011, O_{4} is high for 100, O_{5} is high for 101, O_{6} is high for 110 and O_{7} is high for 111.

Thus the Boolean equations for the outputs of the 3 to 8 decoder shown in Figure 1 are given by:

Equations (1) to (8) show that the decoder of Figure 1 can be designed using AND gate and NOT gate as shown by Figure 2.

This is due to the fact that the output lines are nothing but the logical and of either input (blue lines) or its negation (red lines) with the enable signal (black line).

The analogy presented here for 3 to 8 decoder holds good for any n to 2^{n} decoder.

However, the output bit pattern need not be the same as the one explained.

These kinds of decoders are used in applications such as data multiplexing, seven segment display, and so on.

## Video Explanation of a Binary Decoder

If you prefer a a video explanation, we have explained binary decoders in the video below.