VIPSolutionsProduce an 8 x 3 priority encoder out of 4 x 2 priority encoders, 2 x 1 multipleors and any number of logical gates.
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Produce an 8 x 3 priority encoder out of 4 x 2 priority encoders, 2 x 1 multipleors and any number of logical gates.
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Asked by: rohit singh
Created at: 2025-11-10 20:16:59
Asked by: rohit singh
Created at: 2025-11-10 20:16:59
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# 8x3 Priority Encoder Using 4x2 Priority Encoders
This guide explains how build an **8x3 priority encoder** using:
- **Two 4x2 priority encoders**
- **Two 2x1 multiplexers**
- **Logic gates as needed**
---
## 1. **Block Overview**
- **8-input priority encoder**: Inputs \( D_7 \) (highest) through \( D_ \) (lowest), outputs 3-bit code for the highest active input.
- **4x2 priority encoder**: Inputs \( I_3 \)–\( I_ \), outputs 2-bit code for the highest active input, plus a "valid" output (let's call it \( V \)).
---
## 2. **Partitioning the Inputs**
- **Upper block (Priority Encoder A)**: \( D_7, D_6, D_5, D_4 \)
- **Lower block (Priority Encoder B)**: \( D_3, D_2, D_1, D_ \)
---
## 3. **4x2 Priority Encoder Outputs**
Each 4x2 encoder outputs:
- **2-bit code**: Position of highest-priority input (among its 4).
- **Valid bit (\( V \))**: At least one input is active.
Let:
- **Encoder A outputs**: \( Y_{A1} \) (MSB), \( Y_{A} \) (LSB), \( V_A \)
- **Encoder B outputs**: \( Y_{B1} \) (MSB), \( Y_{B} \) (LSB), \( V_B \)
---
## 4. **Constructing the 3-bit Output**
Let output bits be \( O_2 \) (MSB), \( O_1 \), \( O_ \) (LSB).
### a. **Most Significant Output Bit (\( O_2 \))**
This bit indicates if the upper group (A) has any active input:
- \( O_2 = V_A \)
### b. **Lower Two Output Bits (\( O_1, O_ \))**
Use **multiplexers** to select between encoder A and encoder B based on \( V_A \):
- If \( V_A = 1 \): Use \( Y_{A1}, Y_{A} \) (upper group wins)
- If \( V_A = \): Use \( Y_{B1}, Y_{B} \) (lower group wins)
So,
- \( O_1 = (V_A) \cdot Y_{A1} + (\overline{V_A}) \cdot Y_{B1} \)
- \( O_ = (V_A) \cdot Y_{A} + (\overline{V_A}) \cdot Y_{B} \)
This is achieved with **two 2x1 multiplexers**:
- **MUX for \( O_1 \):**
- Inputs: \( Y_{A1} \), \( Y_{B1} \)
- Select: \( V_A \)
- **MUX for \( O_ \):**
- Inputs: \( Y_{A} \), \( Y_{B} \)
- Select: \( V_A \)
---
## 5. **Block Diagram**
```plaintext
+--------------------------+
| 8x3 Encoder |
+----------+---------------+
|
+-------------+--------------+
| |
[D7-D4] [D3-D]
| |
+-----v-----+ +-----v-----+
| 4x2 Enc A | | 4x2 Enc B |
| | | |
| Y_A1,Y_A | | Y_B1,Y_B |
| V_A | | V_B |
+-----+-----+ +-----+-----+
| |
+----------+ +--------------+
| |
v v
+------+
| MUXs |
+------+
|
(O2,O1,O)
```
_Alt text: Block diagram showing two 4x2 encoders feeding into two multiplexers, producing the 3-bit output._
---
## 6. **Summary Table**
| Output | Expression | Hardware |
|--------|------------------------------------------------|-----------------|
| \( O_2 \) | \( V_A \) | logic gate |
| \( O_1 \) | MUX: \( V_A ? Y_{A1} : Y_{B1} \) | 2x1 multiplexer |
| \( O_ \) | MUX: \( V_A ? Y_{A} : Y_{B} \) | 2x1 multiplexer |
---
## 7. **Logic Summary**
- **Inputs**: \( D_7 \ldots D_ \)
- **Outputs**: \( O_2, O_1, O_ \)
- **Components**: Two 4x2 encoders, two 2x1 multiplexers, simple logic gates.
---
## 8. **Truth Table Example**
| Inputs | Output (\( O_2O_1O_ \)) |
|---------------------------|--------------------------|
| \( D_7=1 \) (others ) | 111 |
| \( D_6=1 \) (others ) | 110 |
| \( D_5=1 \) (others ) | 101 |
| \( D_4=1 \) (others ) | 100 |
| \( D_3=1 \) (others ) | 011 |
| \( D_2=1 \) (others ) | 010 |
| \( D_1=1 \) (others ) | 001 |
| \( D_=1 \) (others ) | 000 |
---
## 9. **Conclusion**
You can construct an **8x3 priority encoder** from two 4x2 priority encoders, two 2x1 multiplexers, and some logic gates by partitioning the inputs, encoding each group, and using the valid signal from the upper group to select outputs.
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