- Binary Decoder Definition: A binary decoder is a logic circuit that converts n binary inputs into 2^n unique outputs.
- Truth Table: A truth table shows the output states of a decoder for every possible input combination.
- Enable Pin: The decoder operates only when the enable pin is high; otherwise, all outputs are low.
- Output Logic: For each input combination, a specific output line goes high, demonstrating the decoder’s function.
- Basic Binary Decoder Applications: Used in data multiplexing, seven-segment displays, and other digital systems.
What is a Binary Decoder?
A binary decoder, also known simply as a decoder, is defined as a combinational logic circuit that converts binary information from n inputs into up to 2n unique outputs. These decoders are widely used in applications like data multiplexing, 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 23 = 8).
The output sequence of a binary decoder for any input pattern is shown in its truth table. A truth table lists the output of a digital logic circuit for all possible input combinations.
Table I shows the truth table for the decoder in Figure 1. It demonstrates that when the enable pin is low, all output lines remain low, regardless of the input sequence.
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 I2I1I0 = 000, the output pin O0 of the decoder is high while all other bits (O7 down to O1) remain low.
Likewise, for the input sequence of 001, only O1 is high. Similar observation shows that only one output line is high for any given input bit pattern i.e.
O2 is high for 010, O3 is high for 011, O4 is high for 100, O5 is high for 101, O6 is high for 110 and O7 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 because the output lines are the logical AND of either the input (blue lines) or its negation (red lines) combined with the enable signal (black line).
The principles explained for the 3 to 8 decoder apply to any n to 2n 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.
