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Introduction to Cascading Multiplexers
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Welcome class! Today we'll explore how to design cascaded multiplexer circuits. Why do you think we might need to cascade multiplexers?
Because sometimes we need to manage more input channels than a single multiplexer can handle?
That's correct! The fundamental idea is to combine several smaller multiplexers to create a larger one. Can anyone tell me how we find out how many smaller multiplexers we need?
I think it's about calculating the difference between the power of two of the desired input channels and the available ones, right?
Exactly! So if we want `2^N` inputs, and `2^n` is what we have, we can use the formula `2^N - n` to determine the number of multiplexers required. Letβs remember this with the acronym 'M=Ns β n'! Now, what comes next after knowing how many multiplexers are needed?
I think we need to connect the selection inputs!
Correct! We connect the less significant bits of the desired multiplexerβs select inputs to the available multiplexer. Good job!
Enabling and Disabling Multiplexers
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Now, letβs discuss the third step about enabling and disabling multiplexers. Who can explain how this is accomplished?
Do we use the leftover bits from the selection inputs to enable or disable multiplexers?
Spot on! This allows only the enabled multiplexer output to contribute to the final output. Who remembers how the outputs get combined?
They get ORed together!
Yes, that's correct! Letβs solidify this by thinking about it as 'Only the active ones add to the voice!' Now letβs explore an example to put these concepts into practice.
Example: Designing a 16-to-1 Multiplexer
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Letβs take Example 8.3 from our material. Can someone summarize how we can construct a 16-to-1 multiplexer using two 8-to-1 multiplexers?
We take two 8-to-1 multiplexers and use the fourth selection input as an ENABLE signal?
Correct! When S_3 is LOW, the upper multiplexer is enabled. If we look at the first eight entries in the truth table, which outputs do we get?
The outputs will be from D0 to D7!
Exactly! And when S_3 is HIGH, what happens then?
We will get outputs from D8 to D15!
Youβre all getting the hang of it! Always remember, we enable or disable based on the selection input state!
Introduction & Overview
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Quick Overview
Standard
Cascading multiplexers enable handling a larger number of input channels than a single multiplexer can accommodate. The section provides a systematic step-by-step guide for constructing larger multiplexer circuits from smaller ones, as well as an example demonstrating the design of a 16-to-1 multiplexer using two 8-to-1 multiplexers.
Detailed
Steps to Design Cascaded Multiplexer Circuits
Cascading multiplexers is a technique used when the number of input channels exceeds the capacity of a single integrated circuit (IC) multiplexer. The main goal is to design multiplexers that can handle extensive input channels, such as combining 8-to-1 multiplexers to create a 16-to-1 or 32-to-1 multiplexer circuit. The essential steps to perform this design are as follows:
- Determine the Number of Multiplexers Needed: If
2^nis the number of input lines of the available multiplexer and2^Nis the required number of input lines for the design, then the number of multiplexers needed can be calculated as2^N - n. - Connect Selection Inputs: Use the least significant bits of the selection inputs of the desired multiplexer to connect to the selection inputs of the available multiplexer.
- Enable or Disable Individual Multiplexers: Remaining bits of the selection inputs of the desired multiplexer are assigned to enable or disable the individual multiplexers. The final outputs from the enabled multiplexers are then ORed to produce the overall output.
Example 8.3
To illustrate this process, we consider designing a 16-to-1 multiplexer using two 8-to-1 multiplexers with active LOW ENABLE inputs. The ENABLE input acts as the fourth selection variable in the most significant bit position. The design essentially involves enabling one of the multiplexers while disabling the other based on the state of S_3, and allows output selection accordingly. The truth table of this concatenated structure aligns with the expected behavior of a 16-to-1 multiplexer.
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Understanding Input Lines in Multiplexers
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If 2^n is the number of input lines in the available multiplexer and 2^N is the number of input lines in the desired multiplexer, then the number of individual multiplexers required to construct the desired multiplexer circuit would be 2^N - n.
Detailed Explanation
This chunk introduces a formula to determine how many individual multiplexers are needed to create a larger multiplexer. We start by recognizing that multiplexers have a power of two number of inputs, denoted by 2^n for a given multiplexer, where 'n' is the number of selection lines. If we want to design a larger multiplexer with 2^N input lines, we can calculate how many smaller multiplexers we need by subtracting the number of available inputs from the larger multiplexer inputs, represented as 2^N - n.
Examples & Analogies
Imagine you want to organize a large party requiring a specific number of chairs, say 16. However, the only chairs you have available are sets of 8. To meet the need, you would require two sets of 8 chairs to have enough for everyone. Similarly, in multiplexers, if you have a specific number of inputs needed, you may calculate how many smaller multiplexers to combine to achieve your goal.
Connecting Selection Inputs
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From the knowledge of the number of selection inputs of the available multiplexer and that of the desired multiplexer, connect the less significant bits of the selection inputs of the desired multiplexer to the selection inputs of the available multiplexer.
Detailed Explanation
In this step, we explain the connection process of the selection inputs when creating a larger multiplexer from smaller multiplexers. It involves utilizing the least significant bits of the selection inputs from the desired multiplexer and linking them to the existing multiplexers. This ensures that the selection process for the inputs operates as intended when deciding which input gets forwarded to the output.
Examples & Analogies
Think about conducting a survey where you have a set of questions (inputs) but only a few response options (available multiplexer). You could take the most straightforward questions (less significant bits) to manage the survey properly while ensuring that every respondent clearly understands their options based on earlier instructions (the existing selection inputs).
Enabling Individual Multiplexers
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The left-over bits of the selection inputs of the desired multiplexer circuit are used to enable or disable the individual multiplexers so that their outputs when ORed produce the final output.
Detailed Explanation
The final step in designing a cascaded multiplexer involves managing the enabling conditions for each multiplexer. The remaining selection bits, which were not used in the previous step, are dedicated to enabling or disabling the individual multiplexers. This ensures only the selected multiplexer conveys its output to the final ORed output, thereby providing a clear and structured output according to the input selection.
Examples & Analogies
Consider a group of performers on stage (the multiplexers) who can only perform when given a signal from a director (the left-over bits). If the director signals to only a few performers, then only those performers will sing, while others remain silent. Therefore, the audience (final output) will only hear from the chosen performers, similar to how a circuit will only output from the enabled multiplexer(s).
Example Design of a Multiplexer
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A 16-to-1 multiplexer can be constructed from two 8-to-1 multiplexers having an active LOW ENABLE input. The ENABLE input is taken as the fourth selection variable occupying the MSB position.
Detailed Explanation
This example illustrates the application of the steps outlined earlier by demonstrating how to create a 16-to-1 multiplexer using two smaller 8-to-1 multiplexers. Here, the fourth selection variable acts as an input signal that determines whether one of the two multiplexers is enabled or disabled. This implementation allows for a larger multiplexer to function correctly using simpler, existing units.
Examples & Analogies
Visualize baking a cake that needs multiple layers (the 16 inputs). You might have two cake pans (the 8-to-1 multiplexers), and you can decide how tall to make each layer depending on how much batter you have (the enable signal) at any given time, ensuring that your final cake meets the desired height.
Definitions & Key Concepts
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Key Concepts
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Cascading: Joining multiple multiplexers to handle more input signals.
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Enable Signal: A control input to activate or deactivate multiplexers in the circuit.
Examples & Real-Life Applications
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Examples
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An example involves constructing a 16-to-1 multiplexer from two 8-to-1 multiplexers, where you utilize the ENABLE input for control.
Memory Aids
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π΅ Rhymes Time
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When input's greater than eight, itβs time to create, cascading multiplexers as the ultimate mate.
π Fascinating Stories
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Imagine a restaurant that serves more dishes than a chef can manage alone; thus, they hire more chefs, just like cascading multiplexers handle more inputs together.
π§ Other Memory Gems
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Remember 'M=Ns β n'! M for multiplexers, N for needs, and n for current status.
π― Super Acronyms
C.E.E - Connect, Enable, and Execute
- The steps to take in designing cascaded multiplexers.
Flash Cards
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Glossary of Terms
Review the Definitions for terms.
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Term: Multiplexer
Definition:
A device that selects one of many input signals and forwards the selected input into a single line.
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Term: Cascading
Definition:
The process of connecting multiple devices to handle larger input sizes than a single device can accommodate.
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Term: Selection Input
Definition:
The designated inputs used to select which signal to output in a multiplexer.
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Term: Enable Input
Definition:
An input that controls whether a multiplexer is activated or inactive.