Universal Gates

Universal Gates

Overview

Universal gates (NAND and NOR) are fundamental building blocks that can be used to implement any other logic function. These gates are called universal because any Boolean function can be constructed using only NAND gates or only NOR gates. This property makes them particularly important in integrated circuit design where standardization of components is crucial.

Detailed Explanation

NAND Gate Implementation

Basic Gates using NAND:

1. NOT Gate:
Input --|NAND|-- Output
       --|   |

2. AND Gate:
A --|NAND|--|NAND|-- Output
B --|   |  |    |

3. OR Gate:
A --|NAND|--|
B --|NAND|--| NAND|-- Output

NOR Gate Implementation

Basic Gates using NOR:

1. NOT Gate:
Input --|NOR|-- Output

2. AND Gate:
A --|NOR|--|
B --|NOR|--| NOR|-- Output

3. OR Gate:
A --|NOR|--|NOR|-- Output
B --|   |

Conversion Table

Function     | NAND Implementation | NOR Implementation
-------------|-------------------|------------------
NOT(A)       | A•A              | A+A
AND(A,B)     | (A•B)')'        | (A'+B')'
OR(A,B)      | (A'•B')'        | (A+B)')'
XOR(A,B)     | See diagram      | See diagram

Circuit Examples

XOR using NAND:

A --|NAND|--|
    |    |  |NAND|--|
B --|    |          |NAND|-- Output
    |    |  |NAND|--|
    |NAND|--|

Practice Problems

  1. Implement these functions using only NAND gates:

    • F = AB + C
    • G = (A + B)(B + C)

  2. Convert these circuits to NOR-only implementation:

    • Half adder
    • 2:1 multiplexer

References

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