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How to Transform a Circuit to Its NAND/NOR Equivalent Form?

Bilal S

Last Modified:

Introduction

Now that we are familiar with all basic forms of representing a function, and their inter-conversion, and inter-conversion through minterms and maxterms, we shall look at transforming a given logic diagram into its equivalent NAND/NOR forms. As the name suggests, this involves converting the original schematic into a version that uses only NAND or NOR gates.

What is an Equivalent Circuit?

An equivalent circuit yields identical outputs for every possible input combination as the original circuit. It behaves the same functionally, even if its internal structure or gate types differ.

Why Convert Logic Diagrams to NAND or NOR Forms?

  1. Universality of NAND and NOR Gates
    • NAND and NOR are universal gates, meaning any digital logic function (AND, OR, NOT, XOR, etc.) can be constructed using only NAND or only NOR gates.
    • This simplifies design and manufacturing, especially when standardizing gate types across a circuit.
  2. CMOS Output Characteristics
    • In CMOS technology, the default output of a gate is typically inverted.
    • Therefore:
      • A NAND gate is the natural CMOS implementation of an AND gate.
      • A NOR gate is the natural CMOS implementation of an OR gate.
    • To produce a true AND or OR gate, designers often invert the output of a NAND or NOR gate.
    • Designing directly with NAND or NOR gates aligns better with CMOS behavior, often resulting in faster and more efficient circuits.

How to Convert to Equivalent NAND/NOR Schematics?

Let’s now explore how to build equivalent logic circuits using only NAND or NOR gates. On these pages, we’ll:

  1. Learn how to implement each basic gate (AND, OR, NOT, etc.) using only NAND or only NOR gates.
  2. Outline a clear, step-by-step method for converting any logic circuit into its NAND-only or NOR-only equivalent.
  3. Walk through a detailed example, reinforcing the conversion process and deepening our understanding of gate-level transformations.

By the end, we’ll be equipped to redesign any digital circuit using just one universal gate type—either NAND or NOR—unlocking powerful techniques for simplification and hardware optimization. Click the relevant links below:

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