Tags: #◇Computer Science #◇CSARCH1 #◇Computer Architecture #◇Combinational Circuits #◇Combinational Circuit - NAND NOR

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Combinational Circuit - NAND/NOR

◇Overview

This sub-module discusses how to implement combinational circuits using NAND/NOR gates.
Objective: Learn how to implement combinational circuits using NAND/NOR gates.

◇Universal Gates

NAND and NOR gates are easier to fabricate with electronic components and are the basic gates used in all IC digital logic families.

• NAND and NOR gates are known as universal gates because they can be used to implement any Boolean function.

◇Logic Gate Conversions

• NAND gate representation of AND gate: Add an inverter to the output line.
• NAND gate representation of OR gate: Add inverters to all input lines.
• NAND gate representation of NOT gate: Tie both inputs of a NAND gate together.
• NOR gate representation of OR gate: Add an inverter to the output line.
• NOR gate representation of AND gate: Add inverters to all input lines.
• NOR gate representation of NOT gate: Tie both inputs of a NOR gate together.

◇NAND Implementation

The implementation of Boolean functions with NAND gates requires that the functions be in Sum-of-Products (SOP) form.

Two-level Implementation

Example: $F = AB + CD$

Multi-level Implementation

Procedure for converting a multilevel AND-OR circuit into an all-NAND gate circuit:

1. Convert all AND gates to NAND gates with AND-invert graphic symbols.
2. Convert all OR gates to NAND gates with invert-OR graphic symbols.
3. Check all the bubbles in the diagram. For each bubble that is not compensated by another small circle along the same line, insert an inverter (a one-input NAND gate) or complement the input literal.

◇NOR Implementation

The implementation of Boolean functions with NOR gates requires that the functions be in Product-of-Sums (POS) form.

Two-level Implementation

Example: $F = (A+B)(C+D)E$

Multi-level Implementation

Procedure for converting a multilevel OR-AND circuit into an all-NOR gate circuit:

1. Convert all OR gates to NOR gates with OR-invert graphic symbols.
2. Convert all AND gates to NOR gates with invert-AND graphic symbols.
3. Check all the bubbles in the diagram. For each bubble that is not compensated by another small circle along the same line, insert an inverter (a one-input NOR gate) or complement the input literal.

◇References & Navigation

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