b) Draw a circuit showing how to use a 74LS138 decoder and a 74LS10 NAND gate to implement the equation F = E(2,5,7). The 74LS138 is an "active-low" decoder and the 74LS10 is a positive logic NAND – remember how to use bubble-matching with NAND gates. In the decoder, Pin G1 is connected to Vcc and the G2 pins are not used (connected to GND). The image on the TI.com datasheet is not very clear, here is a better picture of the decoder: 16

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### Using 74LS138 Decoder and 74LS10 NAND Gate

To implement the equation \( F = \Sigma(2,5,7) \), we'll use a 74LS138 decoder and a 74LS10 NAND gate. The 74LS138 is an "active-low" decoder, and the 74LS10 is a positive logic NAND. Remember to apply bubble-matching with NAND gates for correct logic synthesis. 

### Decoder Configuration

- **Pin G₁**: Connect to \( V_{CC} \).
- **Pins G₂A and G₂B**: Not used, connect to GND.

### 74LS138 Pin Diagram

- **Inputs**:
  - Pin 1: \( A \)
  - Pin 2: \( B \)
  - Pin 3: \( C \)

- **Outputs**:
  - Pin 15: \( Y0 \)
  - Pin 14: \( Y1 \)
  - Pin 13: \( Y2 \) (used in equation)
  - Pin 12: \( Y3 \)
  - Pin 11: \( Y4 \)
  - Pin 10: \( Y5 \) (used in equation)
  - Pin 9: \( Y6 \)
  - Pin 7: \( Y7 \) (used in equation)

- **Other Pins**:
  - Pin 16: \( V_{CC} \)
  - Pin 8: GND

This improved diagram offers a clear view for wiring connections between pins to achieve the desired logic function using the decoder.
Transcribed Image Text:### Using 74LS138 Decoder and 74LS10 NAND Gate To implement the equation \( F = \Sigma(2,5,7) \), we'll use a 74LS138 decoder and a 74LS10 NAND gate. The 74LS138 is an "active-low" decoder, and the 74LS10 is a positive logic NAND. Remember to apply bubble-matching with NAND gates for correct logic synthesis. ### Decoder Configuration - **Pin G₁**: Connect to \( V_{CC} \). - **Pins G₂A and G₂B**: Not used, connect to GND. ### 74LS138 Pin Diagram - **Inputs**: - Pin 1: \( A \) - Pin 2: \( B \) - Pin 3: \( C \) - **Outputs**: - Pin 15: \( Y0 \) - Pin 14: \( Y1 \) - Pin 13: \( Y2 \) (used in equation) - Pin 12: \( Y3 \) - Pin 11: \( Y4 \) - Pin 10: \( Y5 \) (used in equation) - Pin 9: \( Y6 \) - Pin 7: \( Y7 \) (used in equation) - **Other Pins**: - Pin 16: \( V_{CC} \) - Pin 8: GND This improved diagram offers a clear view for wiring connections between pins to achieve the desired logic function using the decoder.
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