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:
- STEP 1: Learn to simplify logic expressions using Karnaugh Mapping (K-Mapping)
- STEP 2: Develop circuits using universal NAND and NOR gates
- 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.
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
Analog Components
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.
Take the Unit 3 Quiz
Universal Gates Overview
NAND Gates
NOR Gates
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
Part 1 Resources
Part 2 Resources
Part 3 Resources