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# Decoder in Digital Electronics

Last Updated on March 21, 2023 by Prepbytes Decoder in Digital Electronics is an essential component that plays a crucial role in the functioning of complex digital systems that are present around us. The working of the decoder circuit is just opposite to the working of the Encoder Circuit. Let us learn about this important component of digital electronics in detail along with various different types of decoders which are commonly used.

## Decoder in Digital Electronics

Decoder in Digital Electronics is defined as a combinational circuit that converts the N inputs into 2N Outputs. In simple terminology, it is just the opposite of an encoder, which converts the 2N inputs to N Outputs. The 2N output lines of the decoder correspond to some binary information. The block diagram of a general decoder is given below for a better understanding of the above-mentioned statements. Various Types of Decoder in Digital Electronics that are commonly used are given below:

## 2 to 4 Decoder in Digital Electronics

A 2 to 4 Decoder in Digital Electronics is the combinational circuit that converts the 2-bit binary information into 4-bit binary information on basis of Enable signal.

Inputs: A0, A1, E
Output: Y0, Y1, Y2, Y3

### Block Diagram of 2 to 4 Decoder in Digital Electronics

Here is the block diagram representing the 2 to 4 Decoder in Digital Electronics. ### Truth Table of 2 to 4 Decoder in Digital Electronics

When the Enable Signal (E) is 1, one of the outputs is 1 and the rest corresponds to 0. Here is the Truth Table for 2 to 4 Decoder in Digital Electronics. From the above truth table, we can write the logical expressions for the output terms as

``````Y3 = E.A1.A0
Y2 = E.A1.A0'
Y1 = E.A1'.A0
Y0 = E.A1'.A0'``````

### Logic Circuit of 2 to 4 Decoder in Digital Electronics

From the above logical expressions, the logical circuit diagram is constructed as. ## 3 to 8 Decoder in Digital Electronics

The 3 to 8 Decoder in Digital Electronics is responsible for converting 3-bit data to 8-bit data. It can be better understood by keeping in mind, that from 3 bits of data, maximum 8 numbers of combinations are possible.

Input: A0, A1, A2
Output: Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7

### Block Diagram of 3 to 8 Decoder in Digital Electronics

The block diagram of 3 to 8 Decoder in Digital Electronics with 3 input lines and 8 Output lines is given below. ### Truth Table of 3 to 8 Decoder in Digital Electronics

Here is the Truth Table for this combinational Circuit. The logical expressions for output signals can be deduced from the above truth table are

``````Y0 = A0'.A1'.A2'
Y1 = A0.A1'.A2'
Y2 = A0'.A1.A2'
Y3 = A0.A1.A2'
Y4 = A0'.A1'.A2
Y5 = A0.A1'.A2
Y6 = A0'.A1.A2
Y7 = A0.A1.A2``````

### Logic Circuit of 3 to 8 Decoder in Digital Electronics

Here is the logic circuit drawn with the help of NOT and AND Logic Gates. ## 4 to 16 Decoder in Digital Electronics

Now since the maximum number of combinations possible from 4 bits is 16. So, the 4 to 16 Decoder in Digital Electronics converts 4-bit input data into 16-bit Output binary information.

This 4 to 16 Decoder is constructed using two 3 to 8 Decoders.

Inputs: A0, A1, A2
Outputs: Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7 Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15

### Block Diagram of 4 to 16 Decoder in Digital Electronics

The block diagram of 4 to 16 Decoder in Digital Electronics using two 3 to 8 Decoders is given below. ### Truth Table of 4 to 16 Decoder in Digital Electronics

Here is the truth table with all possible inputs and outputs. Logical Expressions for output can be deduced as:

``````Y0 = 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``````

### Logic Circuit of 4 to 16 Decoder in Digital Electronics

The logic circuit as per Truth Table and Logical Expressions is given below. ## Applications of Decoder in Digital Electronics

Decoders are used in various digital systems, such as microprocessors, memory units, and various other digital circuits. Here are some of the common applications of decoders:

• Memory Units: Decoders in Digital Electronics are commonly found in memory units like RAM and ROM. A decoder is required by a memory unit to pick a specific memory address for read or write operations. The decoder provides a unique output signal that is used to access a particular memory address.
• Microprocessors: Decoders are used by microprocessors to decode the instruction set. The decoder provides a unique output signal that is used to carry out the instruction. Decoders are also used by the microprocessor to decode addresses and data bus signals.
• Digital Clocks: BCD decoders are used in digital clocks to transform binary-coded decimal codes into decimal codes that indicate hours, minutes, and seconds. For each decimal digit, the BCD decoder outputs a distinct output signal.
• Audio and Video Decoders: Decoders convert digital audio and video information into analog signals that may be played on a speaker or display device. The decoder generates a unique output signal that is used to reconstruct the analog signal.

Conclusion
In conclusion, a decoder in digital electronics is an essential component that is used to convert N numbers into 2N Outputs. The applications of decoders are numerous, and they are widely used in various digital systems, such as microprocessors, memory units, digital clocks, and audio and video decoders. Decoders play a critical role in enabling the proper functioning of these digital systems, and without them, the systems would not be able to operate as intended.