COMPUTER TECH with Mr. Mills
Embedded Files
Logic
Logic
Learning Goals
By the end of this unit you will be able to:
- identify, draw and describe the six main logic gates used in computing
- construct truth tables for logic gates and simple logic circuits
- use logic gates to perform simple mathematical operations utilizing boolean algebra
- recognize the importance of integrated circuits and their impact on the world
Chapter 1
Chapter 1
Intro to Boolean Algebra
Intro to Boolean Algebra
1.1 🎮 Logic Puzzles (generate a new 3x3 Easy Puzzle)
1.2 📺 Circuits & Logic
1.3 📰 Introducing logical equivalence, Article (Khan Academy)
1.4 📰 Equivalent simple Booleans, Article (Khan Academy)
1.5 📖 Write these definitions in your notebook
Boolean
A binary variable, having two possible values, sometimes referred to as “true” (1) or “false” (0).
Truth Table
A diagram made of rows and columns showing all the possible boolean outputs that a given set of boolean inputs can generate.
1.6 📝 Complete these questions in your notebook!
What is the difference between a decimal variable and a binary variable?
Evaluate the following boolean statements:
A. I have two siblings (TRUE/FALSE)
B. The door is shut (TRUE/FALSE)
C. It is raining (TRUE/FALSE)
D. The year 2012 is in the past (TRUE/FALSE)
Describe the which conditions are required for a person to return all TRUE or all FALSE for the statements in question 2.
A blank 2-input (condition) truth table. Note that the first row always starts with both A/B set to 0 or FALSE and the last row has both A/B set to 1 or TRUE.
Chapter 2
Chapter 2
Logic Gates
Logic Gates
2.6 📖 Write these definitions in your notebook
Logic Gate
A device that produces a single Boolean output from one or more inputs
NOT Gate
A device which outputs the opposite of an input signal
OR Gate
A device which outputs a 1 if either of it’s inputs are 1
AND Gate
A device which only outputs a 1 if BOTH inputs are 1
2.7 🎮 Minecraft Logic Gates
Mr. Mills' Intro World (click the download button in the top right corner, then in Minecraft, click IMPORT WORLD and select the file you just downloaded)
Chapter 3
Chapter 3
Logic Circuits
Logic Circuits
3.1 📖 Write these definition in your notebook
Logic Circuit
An electrical device that combines two or more logic gates to produce one or many outputs
3.5 📝 Complete these questions in your notebook!
Create your own logic circuit that uses 3 logic gates of your choice with 3 starting inputs (A, B, C) and one final output (Q).
Create a truth table for the circuit you created.
Chapter 4
Chapter 4
More Logic Gates and Circuits
More Logic Gates and Circuits
4.2 📖 Write these definitions in your notebook
XOR Gate
An eXclusive OR gate, a device that outputs a 1 if and only if one of its inputs are 1, but not if both inputs are 1.
NOR Gate
A negative OR gate, a device that outputs the opposite of an OR gate, i.e. will only output 1 if no inputs are 1.
NAND Gate
A negative AND gate, a device that outputs the opposite of an AND gate, i.e. only outputs a 0 when both inputs are 1.
4.4 📝 Complete these questions in your notebook!
Identify, copy in to your notebook, and label the 6 tables you recognize from the image, with the name of the gate they correspond to.
Can you identify the 7th bonus gate, the XNOR gate?
4.5 ⭐ Extension Task
Using the information from your previous answer, provide an explanation for why we might not use the many of these truth tables for computing purposes.
So far we've learned 6 logic gates (NOT, AND, OR, XOR, NOR, NAND) that generate 6 unique truth tables. However, there are a total of 20 possible output configurations using 1 and 2 bit input logic gates (pictured below)
All 1-input and 2-input logic gate truth tables
All 1-input and 2-input logic gate truth tables
4.8 ⭐ Extension Task
It's possible to create all 2-bit truth tables using just NAND gates. An example is shown for XOR. Can you draw circuits that output the same truth table as:
A. A single AND Gate (easy)
B. A single OR Gate (medium)
C. A single NOR Gate (hard)
This circuit produces the same truth table as an XOR gate, despite it being made entirely of NAND gates.
Checkpoint Quiz
Checkpoint Quiz
Logic Circuits Quiz
Logic Circuits Quiz
This quiz is hosted on Brightspace and will be written in class as per our quiz policy.
Be prepared to demonstrate the following concepts:
Identify the symbols of the first 6 important logic gates
Describe the function and/or purpose of the first logic gates
Construct truth tables for the first 6 important logic gates
Interpret simple logic circuits made from 2 or more logic gates
Chapter 5
Chapter 5
Integrated Circuits
Integrated Circuits
5.2 📖 Write this definition in your notebook
IC
Integrated Circuit, or a microchip. A small electronic device that houses many electronic circuits. Come in many shapes and sizes and are found in nearly all electronic devices.
5.3 📰 How do integrated circuits work, Article (Explain That Stuff) Read and answer the following in your notebook:
What key invention made it possible to squeeze more power into less space in computing?
How are integrated circuits (ICs) described in terms of size and components?
How did integrated circuits address the challenge of linking transistors together in complex circuits?
What does the process of making integrated circuits involve (in terms of creating components on each chip)?
Chapter 6
Chapter 6
Applications of Logic Gates
Applications of Logic Gates
6.1 📽️ How Computers Calculate - the ALU, Video (CrashCourse) until 6:02
6.2 📝 Complete these questions in your notebook from the video
What two logic gates are needed to create a half adder?
Is a full adder just two half adders? Explain.
Why did the original Pac-Man game have an issue when a player reached level 256?
6.3 📖 Write these definitions in your notebook
Half Adder
A logic circuit that adds two binary digits together and outputs a sum and carry bit using 1 XOR and 1 AND gate.
Full Adder
A logic circuit that adds three binary digits together (two inputs and a carry from a previous adder) from two half adders and an additional OR gate, outputting a sum and carry bit
Sum
Output bit of adding two input bits (max = 1)
Carry
Outputs a 1 when the sum of two bits overflows into the next place value
6.10 📖 Write this definition in your notebook
Latch
A device that can remember a single bit of information using sequential (self-looping) logic gates
The pinout for the 74LS76 JK Flip Flop Chip, houses two complete flip flop circuits
Unit Assignment
Unit Assignment
4-bit Adder
4-bit Adder
Build a calculator from scratch!
Build a calculator from scratch!
In this assignment, you'll create your very own calculator from scratch! This sounds simple since the largest numbers you can add together are 1 + 1, but adding in binary requires a lot of logic to handle all of the "carry" bits to the next place value. You will create a simple device that is able to add two 4-bit numbers (i.e. any number from 0 to 15). The inputs will be controlled by switches and the outputs are represented in binary using lights.
You can create this device physically, digitally in TinkerCAD, or digitally in Minecraft!
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