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A combinational circuit is a circuit in which we combine the different gates in the circuit. For example, decoder, encoder, multiplexer and Demultiplexer.

In this article, we will look at a decoder, which is a combinational circuit that converts binary data from N coded inputs to a maximum of 2^N different outputs. It is the opposite of the encoder.

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It is a combinational circuit that converts the N coded input to 2^N coded output. To keep things simple, only one input line is initiated. The binary information is comparable to the 2^N-bit output code. The operation of the decoder is completely the reverse of the encoder.

A digital decoder transfigures a set of digital input signals into a similar decimal code at its output, as the word "decoder" means "to translate or decode coded information from one format into another".

Binary Decoder

A binary decoder is a kind of digital logic device that upholds inputs of 2-bit, 3-bit, or 4-bit codes depending on the number of data input lines; hence a decoder with two or more bits is known as having an n-bit code.

A Binary Decoder transforms coded inputs into coded outputs in which the input and output codes are different, and decoders can "decode" either a Binary or BCD (8421 code) input pattern to a Decimal output code.

2:4, 3:8, and 4:16 line arrangements are common "binary decoder" circuits.

2:4 Binary Decoder

The 2:4 line binary decoder shown below involves two inputs named Q0, Q1 and four outputs P0, P1, P2 and P3. The two binary inputs, Q0 and Q1, are decoded into one of four outputs; thus, they describe a 2:4 binary decoder. Each output represents one of the two input variables' minterms (each output = a minterm).

The truth table for the 2:4 decoder is as follows:

Logical Expression for P3, P2, P1 and P0

P3= Q1Q0
P2= Q0Q1’
P1= Q0’Q1
P0= Q0’Q1’

These four Boolean functions P3, P2, P1 and P0 described above can be implemented using an array of four AND gates.

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3:8 Binary Decoder

The 3:8 line decoder shown below involves three inputs named Q0, Q1, Q2 and Eight outputs P0, P1, P2, P3, P4, P5, P6 and P7. The three binary inputs, Q0, Q1 and Q2, are decoded into one of eight outputs; thus, they describe a 3:8 binary decoder. Each output represents one of the three input variables' minterms (each output = a minterm).


The truth table for the 3:8 decoder is as follows:

Logical Expression for P7, P6, P5, P4, P3, P2, P1 and P0

P0= Q0’Q1’Q2’
P1= Q0’Q1’Q2
P2= Q0’Q1Q2’
P3= Q0’Q1Q2
P4= Q0Q1’Q2’
P5= Q0Q1’Q2
P6= Q0Q1Q2’
P7= Q0Q1Q2

The implementation of these eight boolean functions are as follows:

1. By using eight AND gates



2. Using a 2-to-4 decoder
We can find the number of lower-order decoders required to implement a higher-order decoder using the following formula.
Required no. of lower-order decoder= W2/W1
W1= Number of output in lower-order decode.
W2= Number of output in higher-order decoder.

W1= 4
W2= 8             
Required no. of 2-to-4 decoder=  8/4 =2
i.e  Two 2-to-4 decoders are required in implementing 3:8 decoder.

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Applications of Decoders

  • Decoders are widely used in applications where a specific output or group must be activated only when a particular input combination levels are present. These input levels are frequently provided by the outputs of a register or counter.
  • It is used in code conversions.
  • It is used for data distribution.
  • They are mainly used in logical circuits, data transfer. 

    You can also read about - Shift Registers in Digital Electronics                                       


  1. What is a 4:16 decoder?
    The 4:16 line decoder involves four inputs and sixteen outputs. The four binary inputs are decoded into one of sixteen outputs; thus, they describe a 4:16 binary decoder. It can be implemented by using two 3:8 decoders or three 2:4 decoders.
  2. What is the main function of the decoder?
    Its main function is to convert n lines of input into 2^n lines of output and generate the original signal as output from the coded input signal. An AND gate can be used as the basic decoding element because it produces a high output only when all inputs are high.
  3. Why is decoder used in microprocessors?
    The primary goal of the decoder is to allow for a 'cleaner' representation of the instruction set. As with the direct variant, each instruction represents a single machine function, but using a decoder reduces the number of bits required in the machine code word.

Key Takeaways

This article discussed an overview of a decoder, a combinational circuit that converts the N coded input to 2^N coded output, its types, truth table, the boolean functions using different types of gates, and its applications.

If you are an absolute beginner, interested in coding, and want to learn DSA, you can look for our guided path for DSA, which is free! 
Thank you for reading!

Topics covered
Binary Decoder
2:4 Binary Decoder
3:8 Binary Decoder
Applications of Decoders
Key Takeaways