Implementing a 64:1 MUX Using 16:1 and 4:1 Multiplexers

Implementing a 64:1 multiplexer (MUX) using 16:1 and 4:1 multiplexers requires a structured approach, breaking down the problem into smaller, manageable components. This article will guide you through the process step-by-step.

Understanding the Multiplexer Requirements

A 64:1 MUX takes 64 inputs and selects one of them based on 6 selection lines, as (2^6 64). This means that we need to use selection logic to choose between these 64 inputs.

Step 1: Break Down the Implementation

Step 1: Using 16:1 Multiplexers

A 16:1 MUX can handle 16 inputs and requires 4 selection lines, as (2^4 16). To build a 64:1 MUX, we will use 4 16:1 MUXes. Each 16:1 MUX will handle 16 out of the 64 inputs.

Step 2: Using 4:1 Multiplexers

A 4:1 MUX can handle 4 inputs and requires 2 selection lines, as (2^2 4). We will use a 4:1 MUX to select between the outputs of these 4 16:1 MUXes.

Step 2: Connecting the Multiplexers

Connecting the First Layer of 16:1 MUXes

Connect the 64 inputs to 4 different 16:1 MUXes as follows:

MUX1 will handle inputs 0-15 MUX2 will handle inputs 16-31 MUX3 will handle inputs 32-47 MUX4 will handle inputs 48-63

Use the selection lines S3 S2 S1 S0 to control which of the 16 inputs is output from each MUX.

Connecting the Second Layer 4:1 MUX

The outputs of these 4 16:1 MUXes are connected to the inputs of a single 4:1 MUX. Use the additional selection line S5 to select which of the 4 outputs from the 16:1 MUXes is passed to the final output.

Step 3: Arranging the Selection Lines

The total selection lines needed are 6, which can be arranged as follows:

S5 to select between the 4 outputs of the 16:1 MUXes. S4 S3 S2 S1 S0 to control the 16:1 MUX inputs. The bits S4 S3 will select which 16:1 MUX to use, while S2 S1 S0 will select the input from the chosen 16:1 MUX.

Summary

In summary, the 64:1 MUX is implemented as:

4 x 16:1 MUXes handle the 64 inputs 1 x 4:1 MUX selects the final output from the outputs of the 16:1 MUXes Total selection lines: 6 (S5 S4 S3 S2 S1 S0)

Diagram Representation

Here is a simplified representation of the connections:

Inputs: I0 I1 ... I63Much like this diagram:---------------- |             | | MUX1        | MUX2 |             |  | MUX3        | MUX4 |             | ---------------             |           MUX5             |           Output

This setup allows you to effectively implement a 64:1 MUX using a combination of 16:1 and 4:1 multiplexers.