NAND Only Design

DeMorgan’s Law

Introduction

DeMorgan’s Laws are transformation rules that are used to simplify Boolean expressions. They are essential in digital logic design.

DeMorgan’s Theorems

  • Theorem 1: !(A + B) = !A * !B

  • Theorem 2: !(A * B) = !A + !B

Converting Circuits to NAND Only Design

Why NAND Gates?

NAND gates are universal gates, meaning any Boolean function can be implemented using only NAND gates. This can simplify the manufacturing process and reduce costs.

nand

How do NAND gates simplify circuits?

Example Conversion

Consider the following circuit: Y = (A & B) | C

  1. Identify all the gates in the circuit.

  2. Convert AND gates into NAND gates

  3. Double invert OR gate inputs

  4. Apply DeMorgan’s Theorems to convert OR gate into NAND gates