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Home > Other > 3 to 8 Line Decoder/Demultiplexer Designing Steps, Truth Table, and Ap

# 3 to 8 Line Decoder/Demultiplexer Designing Steps, Truth Table, and Applications

Update Time: 2023-12-01 13:38:01

## Contents

The transformation of binary to decimal can be accomplished using a device known as a decoder. This device belongs to the category of combinational logic circuits and utilizes n-input lines to generate 2n output lines. The output of this device may be less than 2n lines. Binary decoders come in various types, including those with multiple inputs and multiple outputs. Some decoders feature one or more enable inputs besides the data inputs. When the enable input is deactivated, all the outputs become inactive. Based on its purpose, a binary decoder converts data from n-input signals to 2n output signals. In certain decoder types, there are fewer than 2n output lines, leading to the repetition of at least one output pattern for different input values. Higher-order decoders, such as the 3 Line to 8 Line Decoder and the 4 Line to 16 Line Decoder, fall into two categories. This article provides an overview of the 3 Line to 8 Line Decoder.

## What is a Decoder?

The decoder is a combinational logic circuit device with multiple inputs and outputs, categorized into variable decoding and display decoding. Variable decoders typically convert fewer inputs into more outputs, with two common types being n-line-2^n-line decoding and 8421BCD code decoding. Display decoders are employed to convert binary numbers into corresponding seven-segment codes.

Decoding represents the inverse process of encoding. Each binary code is assigned a specific meaning during encoding, signifying a particular signal or object. The reverse process of interpreting the specific meaning from the code state is known as decoding, and the circuit executing this operation is referred to as a decoder. A decoder is a circuit capable of translating the input binary code state into an output signal to convey its original meaning.

Depending on the requirement, the output signal can manifest as a pulse, high or low level. In this article, we discuss 3 to 8 line Decoder and demultiplexer.

Here is the truth table for a basic 1-to-2 line decoder, with A as the input and D0 and D1 as the outputs.

1 to 2 Decoder

The diagram illustrates the logic of the 1-to-2 decoder circuit.

1 to 2 Decoder Circuit

A demultiplexer is a device designed to accept and direct a single input to one of several output lines. This component takes a solitary input data and sequentially chooses one of the individual output lines. It serves as the inverse operation of a multiplexer and is alternatively known as a DEMUX or a data distributor. The DEMUX transforms the input serial data line into parallel output data, generating '2n' outputs for 'n' selection lines with a single input.

DEMUX is employed when a circuit needs to route the data signal to one among multiple devices. In contrast, a decoder is utilized for device selection, whereas a demultiplexer is employed to distribute the signal to numerous devices.

Demux

The following presents the truth table for a 1-to-2 demultiplexer, with "I" representing input data, D0 and D1 as the output data lines and A as the selection line.

1 to 2 Demux Truth Table

The diagram depicts the schematic of the 1-to-2 demultiplexer circuit.

1 to 2 Demux

## The Importance of Decoder

The primary purpose of a decoder is to convert a code into a series of signals, serving as the inverse of an encoder. However, designing decoders is a straightforward process. The key distinction between a decoder and a demultiplexer lies in their functionality—a decoder is a combinational circuit designed to enable only one input and route it to one of the outputs. In contrast, a demultiplexer facilitates multiple inputs and produces the decoded output.

Decoders are crucial in transforming analog signals into digital data for computer processing. Here are instances of encoders and decoders. A binary decoder combines AND, OR, NAND, NOR, and NOT gates to convert an analog signal into binary data.

## What is 3 to 8 Decoder?

The 3-to-8 decoder is a circuit with three input lines and eight (2^3) output lines.

## 3 Line to 8 Line Decoder Designing Steps

In this context, a higher-order decoder, a 3-line to 8-line decoder, is structured using two low-order decoders, such as 2-line to 4-line decoders. Before implementing this decoder, a 2-line to 4-line decoder was devised.

### 2 Line to 4 Line Decoder

This 2-line to 4-line decoder comprises two inputs, A0 and A1, and four outputs labeled Y0 to Y4. The block diagram illustrating this decoder is presented below.

If both the inputs and enable are set to 1, the output will be 1. The truth table for the 2-to-4 decoder is provided below.

 E A1 A0 Y3 Y2 Y1 Y0 0 x x 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0

The output for each condition is expressed as follows:

Y3 = E. A1. A0

Y2 = E. A1. A0′

Y1 = E. A1′. A0

Y0 = E. A1′. A0′

A single product term represents each output from the decoder. To implement these four product terms, four AND gates are utilized. Each gate is equipped with three inputs and two inverters. The logic diagram for the 2-to-4 decoder is illustrated below. Consequently, this decoder's output corresponds to the inputs' minterms when the enable is set to 1. All decoder outputs will be zero if the enable is set to zero. Similarly, a 3-line to 8-line decoder generates eight minterms for the three input variables A0, A1, and A2.

Logic Diagram of 2 to 4 Decoder

### 3 Line to 8 Line Decoder Implementation

To create a 3-line to 8-line decoder, a practical approach involves utilizing a pair of 2-line to 4-line decoders. As previously explained, a 2 to 4-line decoder comprises two inputs and four outputs. Consequently, in the 3-line to 8-line decoder scenario, it encompasses three inputs labeled as A2, A1, and A0, along with eight outputs ranging from Y7 to Y0.

To facilitate the realization of higher-order decoders through lower-order counterparts, the following formula is applied:

The quantity of lower-order decoders needed is determined by m2/m1,

where:

'm1' represents the number of outputs for the lower-order decoder,

'm2' represents the number of outputs for the higher-order decoder.

For example, given m1 = 4 and m2 = 8, substituting these values into the formula yields the required number of decoders as 2. Consequently, to implement a single 3 to 8 decoder, two 2-line to 4-line decoders are essential. The block diagram illustrating this configuration, utilizing two 2 to 4 decoders, is presented below.

3 to 8 Decoder using 2 to 4 Line

The 3-line to 8-line decoder receives parallel inputs denoted as A2, A1, and A0. Simultaneously, the complement of A3 is provided to the enable pin of the decoder, facilitating the generation of outputs designated as Y7 to Y0. These outputs represent the lower eight minterms. Notably, in the decoder above setup, the A3 input is linked to the enable pin, resulting in the acquisition of outputs from Y15 to Y8. Consequently, these outputs correspond to the higher eight minterms.

#### 3 Line to 8 Line Decoder using Logic Gates

Within the 3 to 8 line decoder are three inputs denoted as A, B, and C, while the corresponding outputs are represented by D0, D1, D2...D7.

Determining the eight outputs is contingent upon the values of the three inputs. Thus, the truth table for this 3-line to 8-line decoder is presented below. This truth table reveals that a singular output between D0 and D7 can be chosen based on combining the three select inputs.

 A B C D0 D1 D2 D3 D4 D5 D6 D7 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1

Examining the truth table for the 3-line to 8-line decoder above allows us to articulate the logic expressions as follows:

D0 = A'B'C'

D1 = A'B'C

D2 = A'BC'

D3 = A'BC

D4 = AB'C'

D5 = AB'C

D6 = ABC'

D7 = ABC

Utilizing these Boolean expressions, the 3 to 8 decoder circuit can be realized by incorporating three NOT gates and eight three-input AND gates.

In this circuit, the three inputs undergo decoding to produce eight outputs, each corresponding to a specific minterm of the three input variables.

The three inverters in the logic circuit furnish the complements of the inputs, while each AND gate generates one of the minterms.

This decoder serves the primary purpose of decoding any 3-bit code, yielding eight outputs corresponding to distinct combinations of the input code.

Commonly referred to as a binary-to-octal decoder, this device interprets three-bit binary numbers as inputs, translating them into the eight digits of the octal number system.

## 3 to 8 Decoder Logic Diagram

This decoder circuit furnishes eight logical outputs for three inputs and features an enable pin. Constructed with both AND and NAND logic gates, the circuit processes three binary inputs, activating a singular output among the eight available.

Recognized as a binary-to-octal decoder, the 3 to 8 line decoder circuit operates exclusively when the Enable pin (E) is in a high state. The three distinct inputs, labeled as S0, S1, and S2, dictate the activation of one of the eight outputs—D0, D1, D2, D3, D4, D5, D6, and D7. The logic diagram illustrating the configuration of the 3 to 8 line decoder is depicted below.

## 3 to 8 Line Decoder and Truth Table

The truth table for the 3-to-8 line decoder is provided below.

 S0 S1 S2 E D0 D1 D2 D3 D4 D5 D6 D7 x x x 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0

When the Enable pin (E) is in a low state, all the output pins are also low.

Upon enabling this decoder through the enable input E, one of the eight outputs becomes active for each input combination. The functioning of this 3-line to 8-line decoder can be comprehended by consulting its function table, detailed below.

 Inputs Outputs S0 S1 S2 E D0 D1 D2 D3 D4 D5 D6 D7 x x x 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0

Using this function table, Boolean expressions for each output can be deduced, revealing that each output term involves products of input variables. Consequently, their implementation involves the use of AND gates. The logic circuit diagram for the 3 to 8 decoder is presented in last section.

Operation-wise, the logic circuit of the 3 to 8 decoder follows this description:

• When the enable input (E) is inactive (set to 0), none of the AND gates are operational.

• Upon activating the enable input (E) by setting it to 1, the circuit operates as outlined below:

• When S0 = 0, S1 = 0, and S2 = 0, AND gate 1 activates, yielding output D7.

• When S0 = 0, S1 = 0, and S2 = 1, AND gate 2 activates, yielding output D6.

• When S0 = 0, S1 = 1, and S2 = 0, AND gate 3 activates, yielding output D5.

• When S0 = 0, S1 = 1, and S2 = 1, AND gate 4 activates, yielding output D4.

• When S0 = 1, S1 = 0, and S2 = 0, AND gate 5 activates, yielding output D3.

• When S0 = 1, S1 = 0, and S2 = 1, AND gate 6 activates, yielding output D2.

• When S0 = 1, S1 = 1, and S2 = 0, AND gate 7 activates, yielding output D1.

• When S0 = 1, S1 = 1, and S2 = 1, AND gate 8 activates, yielding output D0.

## 1 to 8 Demultiplexer

A demultiplexer with a single input and eight output lines is known as a 1 to 8 demultiplexer. This device effectively disseminates the input data across eight output lines, contingent upon the chosen input. The input data is denoted as Din, and S0, S1, and S2 represent the select inputs. The resulting outputs are labeled as Y0, Y1, Y2, Y3, Y4, Y5, Y6, and Y7.

The circuit diagram illustrating the configuration of the 1 to 8 demultiplexer is provided below.

## 3 to 8 Decoder/Demultiplexer IC

The IC 74HC238, a 3 to 8 line decoder, is a versatile decoder/demultiplexer in electronic applications. This combinational circuit serves dual purposes, operating as a decoder and a demultiplexer. Specifically, the IC 74HC238 decodes three binary address inputs, namely A0, A1, and A2, translating them into eight corresponding outputs designated as Y0 to Y7. Notably, the device features three Enable pins, enabling its utilization as a demultiplexer with the same configuration.

Other 3 to 8 Line Decoder IC: 74LS138, 74139

### Pin Configuration

Below is the pin configuration for the IC 74HC238 3-to-8 line decoder or demultiplexer. It is a 16-pin DIP.

### Circuit

The logical circuit illustrates the functionality of the IC 74HC238.

### Features of 74HC238 3 to 8 Line Decoder IC

• Broad voltage supply range spanning from 2.0 to 6.0 V

• Efficient CMOS low-power dissipation

• Exceptional resistance to high noise levels

• Capability for demultiplexing

• Convenient multiple input enable for straightforward expansion

• Well-suited for memory chip select decoding applications

• Outputs are actively HIGH and mutually exclusive

• Various package options are available

• Latch-up performance surpasses 100 mA per JESD 78 Class II Level B standards

## Application of Decoder

Decoders find application in scenarios where the activation of specific outputs hinges on the occurrence of precise input code combinations. Several notable applications of decoders include:

• Code conversions utilize decoders effectively.

• Memory systems in computers extensively rely on decoders.

• De-multiplexing or data distribution is a common application of decoders.

• Data routing applications often employ decoders, especially those demanding minimal propagation delay.

• Timing or sequencing purposes benefit from the use of decoders.

• Decoders play a role in turning digital devices on and off at predetermined times.

• Analog decoders were historically employed in analog-to-digital conversion processes.

• Electronic circuits leverage decoders to translate instructions into CPU control signals.

• Logical circuits and data transfer processes prominently feature the use of decoders.

## Applications of Demultiplexer

A demultiplexer holds significant importance as a combinational logic circuit with diverse applications. Some key utilization of demultiplexers are outlined below:

• Demultiplexers are integral in various input and output devices, facilitating efficient data routing.

• Digital control systems employ demultiplexers to select a singular signal from a shared stream of signals.

• Demultiplexers play a role in data transmission within synchronous systems.

• Data acquisition systems benefit from the application of demultiplexers.

• The generation of Boolean functions is achievable using demultiplexers.

• Serial-to-parallel converters find applications for demultiplexers.

• Broadcasting of ATM packets is a notable use case for demultiplexers.

• Establishing connections from a single source to multiple destinations is facilitated by demultiplexers.

• In communication systems, demultiplexers efficiently channel multiple data signals into a single transmission line.

• Arithmetic Logic Units integrate demultiplexers for specific functionalities.

• The design of automatic test equipment is another domain where demultiplexers find practical applications.

## Conclusion

That's the overview of 3 to 8 line decoder and demultiplexers. Designing a 3-to-8 line decoder involves:

1. Systematically following the steps

2. Creating a truth table

3. Deriving Boolean expressions

4. Implementing the circuit

Understanding its applications showcases the versatility of this circuit in various electronic systems, making it a fundamental component in digital design. It is anticipated that you have gained foundational insights into this subject by examining digital logic circuits, truth tables, and their practical applications.

## FAQ

• How many select lines are there for a 3 8 multiplexer?
• 8 select lines.

• How many 3 to 8 decoders are needed to implement a 6 to 64 decoder?
• 9.

• What is the minimum number of gates required to implement a 3 to 8 decoder 1 point 8 12 16 24?
• A decoder circuit necessitates one AND gate for each output, and each AND gate decodes a specific binary number. To illustrate, a 3:8 decoder demands 8 AND gates, with the first AND gate featuring inputs A', B', C', the second A', B', C, the third A', B, C', and so forth.

• What is the difference between an encoder and a decoder?
• A gadget, circuit, or software application that transforms digital information into an analog signal is known as an encoder. Conversely, a decoder is a device, circuit, or program that changes an analog signal into digital data. When it comes to input lines, encoders typically feature a higher count compared to decoders.

• How does a decoder work?
• In a logic circuit with multiple inputs and outputs, a decoder transforms encoded inputs into encoded outputs, with distinct codes for both input and output.

• Can a decoder function as a demultiplexer?
• Utilizing the input lines for data selection and an enable line for data input, the decoder can function as a demultiplexer.

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