Multiplexers, Demuxes, Encoders & Decoders: Design & Applications

TAKEAWAYS:

• Multiplexers select one of n inputs to a single output based on m select lines (e.g., 4:1 MUX uses 2 select lines).
• Demultiplexers do the reverse: take one input and route it to one of n outputs (e.g., 1:4 DEMUX uses 2 select lines).
• Encoders convert n active inputs into a unique m-bit code (e.g., 8:3 priority encoder for interrupt handling).
• Decoders convert m-bit codes back to n active outputs (e.g., 3:8 decoder for memory chip selection).
• Priority encoders resolve conflicts by giving higher-priority inputs precedence (used in CPU interrupt systems).
• BCD-to-7-segment decoders drive LED displays (e.g., in digital clocks or calculators).

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1. Multiplexers (MUX): The Digital "Switchboard"

A multiplexer (MUX) is a combinational circuit that selects one of n inputs and routes it to a single output based on m select lines. It’s like a digital switchboard that picks the right call (input) to send to the operator (output).

How It Works

• Inputs: Data inputs (D0, D1, ..., Dn-1).
• Select Lines: Control which input is passed (S0, S1, ..., Sm-1).
• Output: The selected input (Y).
• Formula: $Y={\sum }_{i=0}^{n-1}(D_i\cdot m_i)$, where $m_i$ is the minterm for the select lines.

Example: 4:1 MUX

Truth Table:

Real-World Use: eSewa Payment Routing

eSewa uses multiplexers to route payment requests from different banks (inputs) to the correct processing unit (output) based on the bank’s ID (select lines). For example:

• If S1S0 = 01 (Nabil Bank), the transaction goes to Nabil’s server.
• If S1S0 = 10 (Global IME), it routes to Global IME’s processor.

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2. Demultiplexers (DEMUX): The Digital "Broadcast"

A demultiplexer (DEMUX) does the opposite of a MUX: it takes one input and routes it to one of n outputs based on select lines. Think of it as a digital broadcast tower sending a signal to one of many receivers.

How It Works

• Input: Single data line (D).
• Select Lines: Determine which output gets the input (S0, S1, ..., Sm-1).
• Outputs: Y0, Y1, ..., Yn-1 (only one is active at a time).

Example: 1:4 DEMUX

Truth Table:

Real-World Use: Daraz Order Fulfillment

Daraz uses demultiplexers to route an order confirmation (input) to the correct warehouse (output) based on the product’s location code (select lines). For example:

• If S1S0 = 10 (Kathmandu warehouse), the order goes there.
• If S1S0 = 01 (Pokhara warehouse), it’s sent there.

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3. Encoders: Converting Signals to Codes

An encoder converts n active inputs into a unique m-bit binary code. It’s like a digital translator that assigns a code to each input signal.

Types of Encoders

1. Simple Encoder: Only one input is active at a time (no priority).
   • Example: 8:3 encoder (8 inputs → 3-bit output).
2. Priority Encoder: Resolves conflicts by giving higher-priority inputs precedence (used in CPU interrupts).

Example: 4:2 Priority Encoder

Truth Table:

Real-World Use: Ncell Interrupt Handling

Ncell’s base stations use priority encoders to handle multiple incoming calls. If two calls arrive simultaneously:

• The call from a higher-priority subscriber (e.g., VIP customer) is processed first.
• The encoder assigns a unique code to the highest-priority active input.

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4. Decoders: Converting Codes to Signals

A decoder converts m-bit binary codes into n active outputs. It’s like a digital dictionary that translates codes into actions.

How It Works

• Inputs: m select lines (S0, S1, ..., Sm-1).
• Outputs: n lines (Y0, Y1, ..., Yn-1), where only one is active for a given input code.
• Formula: $Y_i={\prod }_{j=0}^{m-1}(S_j^{\prime }\text{ or }{S}_j)$ (only one minterm is 1).

Example: 3:8 Decoder

Truth Table:

Real-World Use: Memory Chip Addressing

Computers use 3:8 decoders to select specific memory chips. For example:

• If the CPU sends S2S1S0 = 101, the decoder activates Y5, enabling the memory chip at address 5.
• This is how RAM modules are addressed in systems.

Special Case: BCD-to-7-Segment Decoder

Used in digital clocks and calculators to display numbers. For example:

• Input 0110 (6) lights up segments a, c, f, g, d to display the digit 6.

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5. Comparison Table: MUX vs. DEMUX vs. Encoder vs. Decoder

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6. Worked Example: Design a 4:1 MUX Using Logic Gates

Problem: Implement a 4:1 MUX with inputs D0, D1, D2, D3 and select lines S1, S0.

Solution

1. Truth Table:

   S1	S0	Y
   0	0	D0
   0	1	D1
   1	0	D2
   1	1	D3

2. Boolean Expression: $Y=\overline{S1}\overline{S0}D0+\overline{S1}S0D1+S1\overline{S0}D2+S1S0D3$

3. Circuit Diagram:

   flowchart LR
       A["D0"] --> B["AND"]
       C["D1"] --> D["AND"]
       E["D2"] --> F["AND"]
       G["D3"] --> H["AND"]
       I["S1'"] --> B
       I --> D
       J["S0'"] --> B
       J --> F
       K["S1"] --> D
       K --> H
       L["S0"] --> F
       L --> H
       B --> M["OR"]
       D --> M
       F --> M
       H --> M
       M --> N["Y"]

4. Simplified Using MUX IC: Use a 74LS153 (dual 4:1 MUX) IC to implement this directly.

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7. Worked Example: Design a 3:8 Decoder with Enable

Problem: Implement a 3:8 decoder with an active-low enable (E).

Solution

1. Truth Table:

   E	S2	S1	S0	Y0	Y1	Y2	Y3	Y4	Y5	Y6	Y7
   1	x	x	x	0	0	0	0	0	0	0	0
   0	0	0	0	1	0	0	0	0	0	0	0
   0	0	0	1	0	1	0	0	0	0	0	0
   ...	...	...	...	...	...	...	...	...	...	...	...

2. Boolean Expression for Y0: $Y0=E^{\prime }\cdot \overline{S2}\cdot \overline{S1}\cdot \overline{S0}$

3. Circuit Diagram:

4. Simplified Using Decoder IC: Use a 74LS138 (3:8 decoder with enable) IC.

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In the Real World

1. eSewa Payment Routing

   • What it uses: Multiplexers to route transactions from different banks (inputs) to the correct processing unit (output) based on bank ID (select lines).
   • How: The system checks the bank’s code (e.g., S1S0 = 01 for Nabil Bank) and forwards the payment request to the corresponding server.

2. Daraz Order Fulfillment

   • What it uses: Demultiplexers to route order confirmations to the correct warehouse.
   • How: The order’s location code (e.g., S1S0 = 10 for Kathmandu) activates the corresponding warehouse’s output line.

3. Ncell Base Station Interrupts

   • What it uses: Priority Encoders to handle multiple incoming calls.
   • How: If calls arrive from multiple subscribers, the encoder prioritizes VIP customers (higher input priority) and assigns a unique code to the highest-priority call.

4. Digital Clocks (e.g., Casio)

   • What it uses: BCD-to-7-segment Decoders to display numbers.
   • How: The BCD input (e.g., 0110 for 6) is decoded to light up the correct LED segments (a, c, f, g, d).

5. Computer Memory (RAM)

   • What it uses: Decoders to select specific memory chips.
   • How: The CPU sends an address (e.g., S2S1S0 = 101), and the decoder activates Y5, enabling the memory chip at address 5.

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Exam Tip

1. Understand the Difference:

   • MUX: Many inputs → 1 output (select input).
   • DEMUX: 1 input → Many outputs (select output).
   • Encoder: Many inputs → Few outputs (convert signals to codes).
   • Decoder: Few inputs → Many outputs (convert codes to signals).

2. Priority Encoder Trick:

   • In exams, if asked to design a priority encoder, always prioritize the highest input (e.g., D3 has highest priority in a 4:2 encoder).

3. IC Usage:

   • Memorize common ICs:
     • MUX: 74LS151 (8:1), 74LS153 (dual 4:1).
     • DEMUX: 74LS138 (3:8).
     • Encoder: 74LS148 (8:3 priority).
     • Decoder: 74LS138 (3:8), 74LS47 (BCD-to-7-segment).

4. Truth Tables Are Key:

   • For any design question, start with the truth table. This is what examiners check first.

5. Real-World Applications:

   • Expect questions linking these circuits to payment systems (eSewa), order routing (Daraz), or memory addressing (RAM). Always relate your answer to a real scenario.

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Final Note:

• Practice drawing circuits for MUX, DEMUX, and decoders from truth tables.
• Memorize the IC pinouts (e.g., 74LS138 has an active-low enable).
• Use K-maps if simplifying complex MUX/DEMUX expressions (though most are straightforward).