Designing a 20:1 Multiplexer Using 4:1 Multiplexers

Introduction

Designing a 20:1 Multiplexer (MUX) using smaller 4:1 MUX components is a viable and efficient approach in digital logic design. This article provides a step-by-step tutorial on how to break down a 20:1 MUX into manageable parts using 4:1 MUXes, making the process more feasible and understandable.

Understanding the Components

A 20:1 MUX allows the selection of one line from 20 input lines, while a 4:1 MUX selects one line from 4 inputs. To achieve a 20:1 MUX with the aid of 4:1 MUXes, we need to design a hierarchical system that collectively handles the input and selection logic.

Components Required

5 4:1 MUXes 1 4:1 MUX

Steps to Design

Determine the Number of 4:1 MUXes Needed

N - Since a 20:1 MUX can select from 20 inputs, it can be broken down into smaller MUX units. We can group the 20 inputs into 5 groups of 4 inputs each. Thus, we need 5 4:1 MUXes to handle the first level of selection.

First Level of MUXes

Connections:

MUX0: Inputs I0, I1, I2, I3 MUX1: Inputs I4, I5, I6, I7 MUX2: Inputs I8, I9, I10, I11 MUX3: Inputs I12, I13, I14, I15 MUX4: Inputs I16, I17, I18, I19

Each of these 5 MUXes will produce one output, resulting in 5 outputs let's call them O0, O1, O2, O3, O4.

Second Level MUX

Purpose: Select one of the 5 outputs O0 to O4.

Connection:

Connect O0, O1, O2, O3 to the first 4 inputs of this 6th 4:1 MUX. Handle O4 using a simple logic mechanism.

Final Selection Logic

Selection Lines:

S0 S1: Used for first level MUXs selecting one of the 4 inputs. S2: Used to select which of the first 5 MUX outputs to pass to the final output. S3 S4: Used in conjunction to select outputs.

Managing the 5th Input Selection: To handle the 5th output, use a combination of the selection lines. Use one of the selection lines from the second level MUX to enable the 5th input if the selection indicates that it's the 5th output.

Summary of Selection Lines

S0 S1: Used for selecting one of the 4 inputs in the first level MUXes.

S2: Used to determine the output from the first level MUXes to be passed to the final output.

S3 S4: Used in combination for selecting the final output.

Final Circuit Summary

5 x 4:1 MUXes: For the first level to handle inputs I0 to I19. 1 x 4:1 MUX: For the second level to select from the outputs of the first level. Additional Logic: Required to handle the selection of the 5th input.

This hierarchical approach allows you to effectively use 4:1 MUXes to create a larger 20:1 MUX, making the design process simpler and more manageable.