DE Unit 4: NAND/NOR Design

Universal NAND/NOR gates in circuit design

NAND/NOR DESIGN OVERVIEW

In the last unit, we followed the circuit design process very carefully to develop a digital solution to a problem. In this unit we’ll follow the same process to solve new problems, but we’ll also give ourselves three new tools to work with: K-mapping, universal NAND gates, and universal NOR gates. As we progress, we’ll continue to follow the Circuit Design Process:

  • Define the problem (inputs and outputs)
  • Create the truth table
  • Write the AOI logic expression
  • Simplify the AOI logic expression if we can
  • Draw the circuit diagram
  • Simulate in Multisim to test
  • Build on the breadboard to test and confirm

This process won’t change much, but we’ll have new ways to simplify expressions, and also new types of logic gates to work with. For this unit, you’ll work through three main stages:

  1. STEP 1: Learn to simplify logic expressions using Karnaugh Mapping (K-Mapping)
  2. STEP 2: Develop circuits using universal NAND and NOR gates
  3. STEP 3: Use your new tools to develop a fireplace control circuit

At the end of this unit, you will have learned a new way to simplify expressions that is much simpler than the Boolean algebra from before.  You also will have learned about two new logic gates (NAND and NOR) that will make circuit design quicker in many instances. You also will have gotten to practice the circuit design process on another complete problem.

PART 1: K-MAPPING

(30 pts) About 2 days

As our unit starts, we return to the idea of simplifying logic expressions. Last unit we practiced the ideas of Boolean simplification, but in this unit we get a simpler and more graphical method of simplification: Karnaugh-Mapping (K-Mapping for short)

PART 2: NAND/NOR GATES

(50 pts) About 4 days

As much as we like AND/OR/INVERTER gates, there are other tools at our disposal. In this unit we learn about the NAND and NOR operators, and we also get to look at how those gates can be used in place of any AOI gate we don’t want.  

PART 3: FIREPLACE CONTROL

(40 pts) About 3 days

For your mini-project this unit, you’ll be asked to design the circuit for a fireplace control. You’ll start with a problem situation about building a circuit to control the gas flow to a fireplace. Next, you’ll go through the entire Circuit Design Process to develop, simulate, and breadboard your working circuit!

Part 1: K-Mapping

Learn to simplify logic expressions using pictures rather than algebra

K-Mapping Grid Setups

The first part of our unit returns to logic expressions and simplifying logic expressions. It is important to be able to simplify logic expressions, but as we saw earlier the use of Boolean algebra is both tedious and confusing. For logic expressions with four or fewer inputs, we can use a system called Karnaugh Mapping (K-Mapping for short) to simplify. This part of the unit introduces K-Mapping and gives lots of practice simplifying expressions using both algebra and K-Mapping.

GRADING & PROCESS

Watch the Simplifying Overview and K-Mapping presentation, and take a full page of notes on how to group elements and simplify expressions.

Complete the K-Mapping Assignment.

 Have Mr. Benshoof approve your notes and completed Assignments.

Simplifying With K-Mapping

K-Mapping

K-Mapping Examples

What’s Due In Part 1: K-Mapping

  • K-Mapping Notes
  • K-Mapping Assignment
  • Mr. Benshoof’s Approval

Here’s what’s due in Part 1: K-Mapping

  1.  Good notes on Simplifying and K-Mapping.
  2. Complete the K-Mapping Assignment.
  3. Have Mr. Benshoof approve your notes and assignment.

Part 2: NAND/NOR Gates

Using the universal NAND and NOR gates in circuit design

NAND/NOR Gate Reference

It turns out that if we use AND, OR, and INVERTER (AOI) gates, we can create any circuit combination that we would ever need. Sometimes though, it would be simpler if we didn’t need to use 3 different kinds of gates. The logical expressions NAND and NOR give us new options. Using NAND only, we can replace all AOI gates to have a larger circuit made out of only 1 kind of gate. We can do the same with NOR gates if we want too. This part of the unit explores NAND and NOR gates and demonstrates how we can use them in circuits.

GRADING & PROCESS

 Take a full page of good notes on NAND gates, making particular note of how to substitute NAND gate combinations for our regular AOI gates.

 Complete the NAND Gates Assignment.

 Use Multisim and your breadboard to build the circuits required for the NAND Gates Assignment.

 Take a full page of careful notes on NOR gates, making a special note of how to substitute NOR gate combinations for our regular AOI gates.

 Complete the NOR Gates Assignment.

 Use Multisim and your breadboard to build the circuits required for the NOR Gates Assignment.

 Have Mr. Benshoof check-off your notes, assignments, and circuits.

Universal Gates Overview

NAND Gates

NOR Gates

What’s Due In Part 2: NAND/NOR Gates

  • NAND Notes
  • NAND Gate Assignment
  • NAND Circuits
  • NOR Gate Notes
  • NOR Gate Assignment
  • NOR Circuits
  • Benshoof’s Check-off

Here’s what’s due in Part 2: NAND/NOR Gates

  1. Take a full page of notes on NAND Gates.
  2.  Complete the NAND Gates Assignment.
  3. Create the NAND Gate circuits with Multisim and breadboarding.
  4.  Take a full page of notes on NOR Gates.
  5. Complete the NOR Gates Assignment.
  6.  Create the NOR Gate circuits with Multisim and breadboarding.
  7. Have Mr. Benshoof check-off your notes, assignments, and circuits.

Part 3: Fireplace Control Circuit

Work through the entire circuit design process to solve a problem

Fireplace Control Overview

The last part to our unit gives you the chance to work through an entire circuit design process once again from start to finish. Here you’re asked to develop a circuit that can control the flow of gas to a fireplace based on different safety inputs. You’ll start with the truth table and logic expression, and then use K-Mapping to simplify the expression.  Once that’s done, you’ll develop your circuits using AOI, NAND, and NOR logic as required.  Finally, you’ll simulate the circuit and then breadboard it to show your working circuit!

GRADING & PROCESS

 Read through the Fireplace Control problem carefully and watch the overview video.

 Create a Truth Table that describes the situation in your engineering notebook, then create the corresponding logic expression.

 Simplify your logic expression using K-Mapping.

 Have Mr. Benshoof confirm your simplified logic expression.

 Draw an AOI circuit diagram from your simplified logic expression, and convert some of the circuits to NAND only or NOR only as the assignment specifies.

 Simulate your AOI/NAND/NOR circuits in Multisim

 Breadboard your complete circuit and confirm that it works

 Have Mr. Benshoof confirm your working breadboard circuit.

What’s Due In Part 3: Fireplace Control

  • Truth Table & Expression
  • Mr. Benshoof’s Confirmation
  • Draw Complete Circuit
  • Multisim Circuit
  • Breadboard Circuit
  • Mr. Benshoof’s Check-Off

Here’s what’s due in Part 3: Fireplace Control

  1. Create a Truth Table and simplified logic expression of the Majority Vote problem
  2.  Have Mr. Benshoof confirm your simplified logic expression.
  3.  Draw an AOI circuit diagram from your simplified logic expression, and convert to NAND/NOR as needed.
  4. Simulate your circuit in Multisim
  5.  Breadboard your circuit and confirm that it works
  6. Have Mr. Benshoof confirm your working breadboard circuit.

Double Check: Unit Expectations

Check what you need to have completed by the unit deadline

The purpose of this unit is to give you another experience working through the entire Circuit Design Process. In addition to this, you should also learn three new tools for circuit design: K-Mapping, NAND gates, and NOR gates. Your practice with K-Mapping should give you a tool for simplifying expressions that will continue to be useful. The NAND/NOR Gates are a new tool for building more efficient circuits, and will be something that you can select to use in future circuits.

Engineering Notebook:

(Part 1) You should have taken a full page of notes on Simplifying & K-Mapping.

(Part 2) You should have taken a full page of notes on both NAND Gates and on NOR Gates.

(Part 3) You should have made a Truth Table, logic expression, and simplified the expression for the Fireplace Control Circuit problem in your engineering notebook.

(Part 3) You should have drawn out your AOI/NAND/NOR circuit in your notebook before simulating.

Building & Making:

 (Part 1) You should have completed the K-Mapping Assignment.

 (Part 2) You should have completed the NAND Gates Assignment.

(Part 2) You should have built the NAND circuits in Multisim and on the breadboard to complete the NAND Gates Assignment.

 (Part 2) You should have completed the NOR Gates Assignment.

(Part 2) You should have built the NOR circuits in Multisim and on the breadboard to complete the NOR Gates Assignment.

(Part 3) You should have built your Fireplace Control Circuit in Multisim and confirmed that it works properly.

 (Part 3) You should have built your Fireplace Control Circuit on a breadboard and confirmed that it works properly.

Checkpoints & Quizzes:

(Part 1) Benshoof should have checked-off your notes and completed assignments.

(Part 2) Benshoof should have checked-off your notes, assignments, and circuits.

(Part 3) Benshoof should have confirmed your simplified logic expression.

 (Part 3) Benshoof should have confirmed your working breadboard circuit.