Table of Contents

## Introduction

Demultiplexer has one input and more than one output. It is totally opposite to the multiplexers. It has also selector line to select the output line. Let’s say a demultiplexer have one input and 4 output then it will have two select line to select the which output pin should connect to input pin. It is mostly used in memory multiplexing but there are way more applications of demultiplexer.

Through these selection lines we can choose the output at which input data will available. The number of selector line depends on the number of outputs. If number of selector line is n then number of output line can be 2^{n}.

## 1×2 demultiplexer

It has one input and two output and one selection line. If selection line is low then input data will be available on the first output and if it is high then it will available on the second output.

Truth table of 1×2 de multiplexer –

Now we will write the Boolean expression for this table –

Y_{0} = ES’I

Y_{0} = ESI

Logic diagram –

Considering E high if S is low then input I will provided to Y_{0} output and if it is high then input I will output through the Y_{1}.

## 1×4 demultiplexer

As it name suggests in this de-multiplexer number of input will be one and number of output will be 4. Let’s calculate the number of selector lines. Say N number of outputs and M is number of selector line.

N = 4

M = 2.1

M =2

So, here will be 2 selection line.

Truth table of 1×4 de-multiplexer –

Boolean expression for this table –

Y_{1} = ES_{1}’S_{0}I

Y_{0} = ES_{1}’S_{0}’I

Y_{2} = ES_{1}S_{0}’I

Y_{3} = ES_{1}S_{0}I

Logic diagram of 1×4 de multiplexer –

## 1×8 demultiplexer

In this de-multiplexer input line will be one and output line will be 8. This is why it is called 21×8 De Multiplexer. Let’s calculate the selection line. Say N is the number of output line and M is the number of selection line.

N = 8

M = 3

We need 3 selection line.

Truth table of the 1×8 De Multiplexer –

Boolean expression for the 1×8 de-multiplexer –

Y_{0} = ES_{2}’S_{1}’S_{0}’I Y_{1} = ES_{2}’S_{1}’S_{0}I

Y_{2} = ES_{2}’S_{1}S_{0}’I Y_{3} = ES_{2}’S_{1}S_{0}I

Y_{4} = ES_{2}S_{1}’S_{0}’I Y_{5} = ES_{2}S_{1}’S_{0}I

Y_{6} = ES_{2}S_{1}S_{0}’I Y_{7} = ES_{2}S_{1}S_{0}I

Logic diagram of 1×8 De Multiplexer –

## Demultiplexer applications

There are some useful applications of demultiplexer in creating combinational logic circuits like memory and other decoding circuits. Let’s see some of its applications.

### Full subtractor using 1×8 demultiplexer

We can implement a full subtractor using a 1×8 de multiplexer. Let’s first see the truth table for full subtractor.

SOP form expression for the difference and borrow bit.

D(X, Y, B_{i}) = Σm(1, 2, 4, 7)

B(X, Y, B_{i}) = Σm(1, 2, 3, 7)

As we know that only one output of de multiplexer will be high at a time if we provide high input. Considering S_{0}, S_{1} and S_{2} as X, Y, B_{i} respectively, tie up all the de multiplexer output with input of OR gate according to SOP expression of D. That is our D output of full subtractor. And repeat the same process for the borrow output.

### Full adder using 1×8 demultiplexer

We can implement a full adder using a 1×8 de multiplexer. Let’s first see the truth table for full adder.

SOP form expression for the difference and borrow bit.

S(X, Y, B_{i}) = Σm(1, 2, 4, 7)

C_{o} (X, Y, B_{i}) = Σm(3, 5, 6, 7)

As we have done previously, we will connect the appropriate outputs of de multiplexer with inputs of OR gate such that its output is same as full adder.

### Demultiplexer as a decoder

We can implement the decoder using the demultiplexer. But before that first let’s see what decoder is.

The figure above is 2×4 decoder. Which has two input and four output. Let’s see the truth table.

Difference in the decoder and demultplexer is just that in multiplexer there are selection line for selecting output and in the decoder output is selected through the inputs.

So, if we connect the input of de multiplexer with high voltage then it will work as a decoder.

Debra RoseThis design is steller!

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know how to keep a reader entertained. Between your

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I really loved what you had to say, and more than that, how

you

presented it. Too cool!