Lecture: Implementing Boolean Functions with CMOS Logic

Introduction

• Channel: ALL ABOUT ELECTRONICS
• Topic: Implementing complex Boolean functions using CMOS logic.
• Previous Video: Designing logic gates using CMOS logic.

Key Concepts

• CMOS logic can be used to design complex Boolean functions.
• Examples will be used to demonstrate the implementation.

Example 1: Finding the Boolean Expression

• Logic function implemented with CMOS circuit provided.
• PMOS Network: Pulls output voltage to logic 1.
• NMOS Network: Pulls output voltage to logic 0.
• Expression for NMOS Network:
  • Output Y is 0 when C = 1 and either A or B = 1.
  • Boolean expression: Yᵇar = C • (A + B)
  • Simplified to: Y = (C • (A + B))ˉ
• Expression for PMOS Network:
  • Output connected to Vdd when C = 0 or (Aand B = 0).
  • Boolean expression: Y = C' + (A' • B')
• Conclusion: From both networks, the implemented function is the same.
  • Correct answer: A

Example 2: Three-input NAND Gate

• Given CMOS logic circuit to find the Boolean expression.
• Recognized as a three-input NAND gate with inputs A, B, and C' taking the output.
• NMOS Network: Pulls output to logic 0 when A = 1, B = 1, and C' = 1.
• Boolean Expression:
  • Y = (A • B • C')ˉ
  • Simplifies to: Y = A' + B' + C
  • Correct answer: A

Example 3: NMOS Logic Gate

• Circuit given to find the logic function implemented.
• Pull-up Network: Single NMOS transistor acts as a pull-up.
• Pull-down Network: Complex arrangement with transistors A, B, C (parallel), and D, E (series).
• Expression for NMOS Network:
  • Y = 0 when A = 1 and (either B or C = 1), or when D = 1 and E = 1.
  • Boolean expression: Y' = (A • (B + C) + D • E)
  • Simplifies to: Y = (A • (B + C) + D • E)ˉ
  • Correct answer: C

Example 4: Specific NMOS Network Values

• Given C and D inputs are 0.
• Find values of A and B for Y = 0.
• NMOS Network: Path to ground connected when both A and B are 1.
• Correct answer: C

Example 5: CMOS Based Logic Circuit

• Identify logic function for given circuit.
• PMOS and NMOS Networks: Inputs connected through NOT gates.
• Expression for NMOS Network:
  • f = 0 when (X' • Y') or (X • Y).
  • Boolean expression: f' = (X' • Y' + X • Y)
  • Recognized as XOR function: f = (X ⊕ Y)
  • By interchanging inputs, can implement XNOR function.
  • Correct answer: D

Example 6: Tri-State Buffer

• Circuit given to find functionality with enable inputs 0 and 1.
• Enable = 0:
  • Inputs to NAND gate: 0 and D.
  • PMOS transistor remains OFF (high impedance).
• Enable = 1:
  • Inputs to NAND gate: 1 and D.
  • NMOS transistor acts as inverter, output = D.
  • Circuit functions as Tri-State Buffer.
  • Correct answer: B

Example 7: Simplifying and Finding Boolean Expression

• Circuit provided, find functionality.
• PMOS and NMOS Arrangement: Identified inputs and connections.
  • Expression: F = (A • B + A' • B')
  • Recognized as XNOR function.
  • Correct answer: XNOR function.

Conclusion

• Understand implementation of complex logic functions with CMOS logic.
• Practical applications and design concepts.
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