# Decoder Circuit with truth table – Digital Systems

## Introduction

Decoders are the combinational logic circuits that intake binary codes, decodes them and produces an output. In other words we can say that decoders are the circuits that perform the opposite operation of the encoders.

A decoder converts $2^{n}$ numbers of output from n number of inputs.

### 2 line to 4 line decoder:

2 line to 4 line converts 2 line inputs into 4 line outputs.

The block diagram of 2 line to 4 line decoder is given below.

In the above diagram A and B are the inputs to the decoder and D0, D1, D2 and D3 are the outputs of decoder.

The truth table of this circuit is given below.

From the above truth table

D0 = $\overline{A}.\overline{B}$

D1 = $\overline{A}.B$

D2 = $A.\overline{B}$

D3 = A.B

So the logic diagram of 2 line to 4 line decoder is as below.

### 3 line to 8 line decoder:

3 line to 8 line decoder has 3 inputs and 8 outputs.

The block diagram of 3 to 8 line decoder is given below.

In the above diagram A, B and C are the inputs to the decoder and D0, D1, D2, D3, D4, D5, D6 and D7 are the outputs of the decoder.

The truth table of this circuit is given below.

From the above truth table

D0 = $\overline{A}.\overline{B}.\overline{C}$

D1 = $\overline{A}.\overline{B}.C$

D2 = $\overline{A}.B.\overline{C}$

D3 = $\overline{A}.B.C$

D4 = $A.\overline{B}.\overline{C}$

D5 = $A.\overline{B}.C$

D6 = $A.B.\overline{C}$

D7 = A.B.C

So the logic diagram of 3 to 8 line decoder is as below.

### Applications of Decoders:

Decoders are used to produce a group of outputs from a particular combination of inputs. These circuits are used to drive Dc motors, relays and LEDs. Decoders are also used as an address pointer in the memory of computers.

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