Implementing a 64:1 Multiplexer Using Eight 8:1 Multiplexers

To implement a 64:1 multiplexer (MUX) using eight 8:1 MUXes, you can use a hierarchical approach. This method leverages the functionality of the 8:1 MUX to construct a larger 64:1 MUX. Below, we will guide you through the process step by step.

Step 1: Understanding the Components

An 8:1 MUX has 8 input lines, 3 select lines, and 1 output. Similarly, a 64:1 MUX has 64 input lines, 6 select lines, and 1 output.

Step 2: MUX Configuration

First Level

To handle the 64 inputs, you need to use eight 8:1 MUXes. Each 8:1 MUX will process 8 of the 64 inputs. Here's how you can connect them:

MUX0: Inputs 0 to 7 MUX1: Inputs 8 to 15 MUX2: Inputs 16 to 23 MUX3: Inputs 24 to 31 MUX4: Inputs 32 to 39 MUX5: Inputs 40 to 47 MUX6: Inputs 48 to 55 MUX7: Inputs 56 to 63

At the first level, each 8:1 MUX will produce 8 outputs.

Second Level

At the second level, one 8:1 MUX will select from the outputs of the first level MUXes. This second-level MUX will have the outputs from the eight 8:1 MUXes as its inputs. This configuration effectively combines the outputs of the first-level MUXes to produce a final output.

Step 3: Select Lines Configuration

First Level

Use the 3 select lines (S2, S1, S0) for the first level. Each 8:1 MUX in the first level will use these select lines to determine which of its 8 inputs is selected.

Second Level

For the second level, use an additional select line (S3) to select which of the 8 outputs from the first level MUXes is passed to the final output.

Step 4: Select Line Mapping

The select lines for the 64:1 MUX should be mapped as follows:

S3: This select line will determine which of the eight 8:1 MUX outputs is selected. S2, S1, S0: These select lines will determine which of the 8 inputs is selected within the chosen 8:1 MUX.

Step 5: Summary of Connections

Inputs to MUXes: MUX0: Inputs 0 to 7 MUX1: Inputs 8 to 15 MUX2: Inputs 16 to 23 MUX3: Inputs 24 to 31 MUX4: Inputs 32 to 39 MUX5: Inputs 40 to 47 MUX6: Inputs 48 to 55 MUX7: Inputs 56 to 63 Select Lines: S3: Connect to the select line of the second level MUX. S2, S1, S0: Connect to the select lines of the first level MUXes. Final Output: The output from the second level MUX is the final output of the 64:1 MUX based on the select lines S3, S2, S1, and S0.

Diagram Representation

Here is the diagram to illustrate the process:

Inputs: 0-63

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First Level 8:1 MUXes MUX0 to MUX7

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MUX0 MUX1 MUX2 MUX3 MUX4 MUX5 MUX6 MUX7

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Second Level 8:1 MUX

Final Output

This structure allows you to effectively create a 64:1 multiplexer using eight 8:1 multiplexers. By breaking down the 64:1 MUX into smaller, manageable units, you can achieve the desired functionality with a hierarchical design.