Decoder | Digital Circuits - Electronics and Communication Engineering (ECE) PDF Download

What is Decoder?

The combinational circuit that change the binary information into 2^N output lines is known as Decoders. The binary information is passed in the form of N input lines. The output lines define the 2^N-bit code for the binary information. In simple words, the Decoder performs the reverse operation of the Encoder. At a time, only one input line is activated for simplicity. The produced 2^N-bit output code is equivalent to the binary information.

There are various types of decoders which are as follows:

2 to 4 line decoder

In the 2 to 4 line decoder, there is a total of three inputs, i.e., A₀, and A₁ and E and four outputs, i.e., Y₀, Y₁, Y₂, and Y₃. For each combination of inputs, when the enable 'E' is set to 1, one of these four outputs will be 1. The block diagram and the truth table of the 2 to 4 line decoder are given below.

Block Diagram
Truth Table
The logical expression of the term Y₀, Y₀, Y₂, and Y₃ is as follows:
Y₃ = E.A₁.A₀
Y₂ = E.A₁.A₀'

Y₁ = E.A₁'.A₀
Y₀ = E.A₁'.A₀'
Logical circuit of the above expressions is given below:

3 to 8 line decoder

The 3 to 8 line decoder is also known as Binary to Octal Decoder. In a 3 to 8 line decoder, there is a total of eight outputs, i.e., Y₀, Y₁, Y₂, Y₃, Y₄, Y₅, Y₆, and Y₇ and three outputs, i.e., A₀, A₁, and A₂. This circuit has an enable input 'E'. Just like 2 to 4 line decoder, when enable 'E' is set to 1, one of these four outputs will be 1. The block diagram and the truth table of the 3 to 8 line encoder are given below.

Block Diagram
Truth Table
The logical expression of the term Y0, Y1, Y2, Y3, Y4, Y5, Y6, and Y7 is as follows:
Y₀ = A₀'.A₁'.A2'
Y₁= A₀.A₁'.A₂'
Y₂ = A₀'.A₁.A₂'
Y₃ = A₀.A₁.A₂'
Y₄ = A_0'.A₁'.A₂
Y₅ = A₀.A₁'.A₂
Y₆ = A₀'.A₁.A₂
Y₇ = A₀.A₁.A₂
Logical circuit of the above expressions is given below:

4 to 16 line Decoder

In the 4 to 16 line decoder, there is a total of 16 outputs, i.e., Y₀, Y₁, Y₂,……, Y₁₆ and four inputs, i.e., A₀, A₁, A₂, and A₃. The 3 to 16 line decoder can be constructed using either 2 to 4 decoder or 3 to 8 decoder. There is the following formula used to find the required number of lower-order decoders.

Required number of lower order decoders = m₂/m₁
m₁ = 8
m₂ = 16
Required number of 3 to 8 decoders=Decoder=2

Block Diagram

Truth Table
The logical expression of the term A0, A1, A2,…, A15 are as follows:
Y_{0 =} A₀'.A₁'.A₂'.A₃'
Y₁ = A₀'.A₁'.A₂'.A₃
Y₂ = A₀'.A₁'.A₂.A₃'
Y₃ = A₀'.A₁'.A₂.A₃
Y₄ = A₀'.A₁.A₂'.A₃'
Y₅ = A₀'.A₁.A₂'.A₃
Y₆ = A₀'.A₁.A₂.A₃'
Y₇ = A₀'.A₁.A₂.A₃
Y₈ = A₀.A₁'.A₂'.A₃'
Y₉ = A₀.A₁'.A₂'.A₃
Y₁₀ = A₀.A₁'.A₂.A₃'
Y₁₁ = A₀.A₁'.A₂.A₃
Y₁₂ = A₀.A₁.A₂'.A₃'
Y₁₃ = A₀.A₁.A₂'.A₃
Y₁₄ = A₀.A₁.A₂.A₃'
Y₁₅ = A₀.A₁.A₂'.A₃ 
Logical circuit of the above expressions is given below: