# Encoders

An encoder can also be described as a combinational circuit that performs the inverse operation of a decoder. An encoder has a maximum of 2^n (or less) input lines and n output lines.

In an Encoder, the output lines generate the binary code corresponding to the input value.

The following image shows the block diagram of a 4 * 2 encoder with four input and two output lines.

The truth table for a 4-to-2 line encoder can be represented as:

A3 A2 A1 A0 D1 D0
0 0 0 1 0 0
0 0 1 0 0 1
0 1 0 0 1 0
1 0 0 0 1 1

From the truth table, we can write the Boolean function for each output as:

D1 = A3 + A2
D0 = A3 + A1

The circuit diagram for a 4-to-2 line encoder can be represented by using two input OR gates.

The most common application of an encoder is the Octal-to-Binary encoder. Octal to binary encoder takes eight input lines and generates three output lines.

The following image shows the block diagram of an 8 * 3 line encoder.

The truth table for an 8 * 3 line encoder can be represented as:

D7 D6 D5 D4 D3 D2 D1 D0 x y z
0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0 1
0 0 0 0 0 1 0 0 0 1 0
0 0 0 0 1 0 0 0 0 1 1
0 0 0 1 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 1 0 1
0 1 0 0 0 0 0 0 1 1 0
1 0 0 0 0 0 0 0 1 1 1

From the truth table, we can write the Boolean function for each output as:

x = D4 + D5 + D6 + D7
y = D2 + D3 + D6 + D7
z = D1 + D3 + D5 + D7

The circuit diagram for an 8 * 3 line encoder can be represented by using two input OR gates.

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