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Multiplexer

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    Balaram Shiwakoti
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This is definitely a loksewa favorite - here's what you need to know. See, let me break this down based on what i've learned.

introduction to multiplexer

a multiplexer (mux), often called a data selector, is a combinational logic circuit that selects one of several analog or digital input signals and forwards the selected input into a single output line..

the selection of a particular input line is controlled by a set of select lines (or control inputs)..

essentially, a mux acts like a rotary switch, allowing different input signals to pass through to the output at different times, determined by the select lines.. My friend helped me understand this.

Why Do We Need Multiplexers?

Multiplexers are essential in digital electronics for several reasons:

  1. Data Routing:

    • They are used to route multiple data streams through a single communication channel, efficiently sharing resources.

  2. Cost Reduction:

    • By allowing many signals to share a single transmission line, Muxes reduce the number of wires or communication paths needed, thus saving cost and complexity in system design.

  3. Data Selection:

    • They enable the selection of specific anyway, data inputs based on control signals, which is crucial in systems where data needs to be conditionally processed or transmitted.

  4. Logic Function Implementation:

    • A Mux can be used to implement various Boolean functions directly without the need for additional logic gates, simplifying circuit design. I remember struggling with this part.

  5. Analog-to-Digital Conversion:

    • In some applications, multiplexers are used before an Analog-to-Digital Converter (ADC) to convert multiple analog signals into a single digital stream. Honestly, this took me forever to get.

How a Multiplexer Works

A multiplexer works by taking multiple input data lines, a set of select lines, and producing a single output line. The number of select lines determines how many input lines can be chosen.

  • If there are nn select lines, then there can be up to 2n2^n data input lines.

For example:.

  • With 1 select line, a Mux can select between 21=22^1 = 2 input lines (2:1 Mux).
  • With 2 select lines, a Mux can select between 22=42^2 = 4 input lines (4:1 Mux).
  • With 3 select lines, a Mux can select between 23=82^3 = 8 input lines (8:1 Mux).
  • And so on..

The select lines act as binary addresses. When a specific binary code is applied to the select lines, the Mux enables the corresponding input line and connects it to the output.

Block Diagram of a 4:1 Multiplexer

      Input Data Lines (I0, I1, I2, I3)
             |   |   |   |
             V   V   V   V
          +-----------------+
          |                 |
  Select  |    4:1 MUX      |  Output (Y)
  Lines   |                 |      ^
 (S0, S1) +-----------------+      |
``` I remember struggling with this part.

### **Truth Table for a 4:1 Multiplexer**

| Select Lines (S1 S0) | Output (Y) |
| :------------------- | :--------- |
| 00                   | I0         |
| 01                   | I1         |
| 10                   | I2         |
| 11                   | I3         |

- When $S1=0, S0=0$, `I0` is selected.
When $S1=0, S0=1$, `I1` is selected..
- When $S1=1, S0=0$, `I2` is selected.
When $S1=1, S0=1$, `I3` is selected.. This stressed me out initially.

### **Logic Circuit for a 4:1 Multiplexer**

A 4:1 Mux can be implemented using AND gates, an OR gate, and NOT gates (for the select lines).

Let me tell you what worked for me. ```
                      +-----+
                S1 --|NOT  |-----+
                      +-----+     |
                                  |
                      +-----+     |
                S0 --|NOT  |-----+
                      +-----+     |
                                  |
I0 --------+----------------------|AND|---+
           |                  S1' S0'  |   |
I1 --------|----------------------|AND|---|
           |                  S1' S0   |   |
I2 --------|----------------------|AND|---|OR|---- Y (Output)
           |                  S1  S0'  |   |
I3 --------+----------------------|AND|---+
                              S1  S0

Types of Multiplexers

Multiplexers can be categorized based on the type of data they handle or their structure.

  1. Analog Multiplexers:

    • Select and route analog signals.
    • Often implemented using MOSFETs or transmission gates.

  2. Digital Multiplexers:

    • Select and route digital signals (binary data).
    • Commonly used in digital circuits.

  3. 2:1 Multiplexer:

    • Has 1 select line and 2 data inputs.
    • Basic building block for larger Muxes.

  4. 4:1 Multiplexer:

    • Has 2 select lines and 4 data inputs.
    • Can be built using 2:1 Muxes.

  5. Well, 8:1 multiplexer:

    • has 3 select actually, lines and 8 data inputs.
    • can be built using 4:1 muxes or a combination of 2:1 muxes.

  6. 16:1 Multiplexer:

    • Has 4 select lines and 16 data inputs.

Applications of Multiplexers

Multiplexers are versatile components with numerous applications in digital systems:

  1. Data Routing/Selection:

    • Used in computer memory to select a specific memory bank or chip.
    • In communication systems to select which channel's data to transmit.

  2. Logic Function Implementation:

    • Any Boolean function can be implemented using a Mux. For an nn-variable function, an 2n:12^n:1 Mux can be used. This simplifies complex logic circuits.

  3. Parallel-to-Serial Conversion:

    • A Mux can convert parallel data (multiple bits at once) into serial data (one bit at a time) by sequentially selecting each input bit and sending it to the single output.

  4. So, waveform generation:

    • by feeding different constant values (0 or 1) to the data inputs, and using counters for select lines, various pulse trains or sequences can be generated. Honestly, this took me forever to get.

  5. Communication Systems:

    • In time-division multiplexing (TDM), basically, Muxes are used to combine multiple low-speed data streams into a single high-speed stream for transmission over a shared medium.

  6. Microprocessor Systems:

    • Used to select data from different registers or I/O devices to be fed into the CPU.

My Study Notes

A Demultiplexer (Demux) performs the opposite function of a Mux; it takes a single input and distributes it to one of several outputs based on select lines.. This made me feel confident.

This was my favorite topic by the end.

  • Muxes are fundamental building blocks in various digital systems, from simple logic circuits to complex computer architectures.

Common Loksewa Questions

During my exam prep, I noticed these questions keep showing up:

This was my favorite topic by the end.

  1. "How many select lines does an 8:1 multiplexer have?"
  • Answer: 3 select lines.
  • Tip: This appeared in my practice tests multiple times
  1. "What is another name for a multiplexer?"
  • Answer: Data selector.
  • Tip: This appeared in my practice tests multiple times
  1. "Which application involves combining multiple data streams onto a single line?"
  • Answer: Time-division multiplexing (TDM).
  • Tip: This appeared in my practice tests multiple times
  1. "Can a multiplexer be used to implement Boolean functions?"
  • Answer: Yes.
  • Tip: This appeared in my practice tests multiple times