This document discusses encoders and provides examples of 4-to-2 and 8-to-3 line encoders. It defines an encoder as a combinational circuit that performs the reverse operation of a decoder, with a maximum of 2n input lines and n output lines. Truth tables and logic circuits are given for 4-to-2 and 8-to-3 line encoders. Uses of encoders include converting decimal to binary numbers to perform binary operations like addition and subtraction in digital systems.

1. P R O F . N E E R A J B H A R G A V A
M R S . P O O J A D I X I T
D E P A R T M E N T O F C O M P U T E R S C I E N C E ,
S C H O O L O F E N G I N E E R I N G & S Y S T E M
S C I E N C E S
M D S U N I V E R S I T Y A J M E R , R A J A S T H A N
Encoder

2. Introduction
 An Encoder is a combinational circuit that performs
the reverse operation of Decoder.
 It has maximum of 2n input lines and ‘n’ output
lines. It will produce a binary code equivalent to the
input, which is active High.
 Therefore, the encoder encodes 2n input lines with ‘n’
bits. It is optional to represent the enable signal in
encoders.

3. 4 to 2 Encoder
 Let 4 to 2 Encoder has four inputs Y3, Y2, Y1 & Y0 and
two outputs A1 & A0.
 The block diagram of 4 to 2 Encoder is shown in
the following figure.

4. 4 to 2 Encoder
 The Truth table of 4 to 2 encoder

5. 4 to 2 Encoder
 The logical expression of the term A0 and A1 is as follows:
 A1=Y3+Y2
A0=Y3+Y1
 Logical circuit of the above expressions is given below:

6. 8 to 3 line Encoder:
 The 8 to 3 line Encoder is also known as Octal to Binary Encoder.
In 8 to 3 line encoder, there is a total of eight inputs, i.e., Y0, Y1, Y2, Y3,
Y4, Y5, Y6, and Y7 and three outputs, i.e., A0, A1, and A2. In 8-input lines,
one input-line is set to true at a time to get the respective binary code in
the output side. Below are the block diagram and the truth table of the
8 to 3 line encoder.
 Block Diagram:

7. 8 to 3 line Encoder:
 Truth Table:

8. 8 to 3 line Encoder:
 The logical expression of the term A0, A1, and A2 are as follows:
 A2=Y4+Y5+Y6+Y7
A1=Y2+Y3+Y6+Y7
A0=Y7+Y5+Y3+Y1
 Logical circuit of the above expressions is given below:

9. Uses of Encoders:
 These systems are very easy to use in all digital
systems.
 Encoders are used to convert a decimal number into
the binary number. The objective is to perform a
binary operation such as addition, subtraction,
multiplication, etc.