Binary Lessons
Binary Addition
In this lesson, students will learn how to add two 8‐bit binary integers and explain overflow errors which may occur.
Learning Objectives:
Suggested time: 50 mins
Curriculum Mapping:
Learning Objectives:
- add two 8‐bit binary integers and explain overflow errors which may occur
Suggested time: 50 mins
Curriculum Mapping:
KS3 Computing:
- Understand how numbers can be represented in binary, and be able to carry out simple operations on binary numbers (e.g. binary addition, conversion between binary and decimal) → Binary addition is explicitly listed as a required skill.
GCSE (KS4) Computer Science – OCR J277:
- Convert positive denary whole numbers to binary (up to 8 bits) and vice versa
- Add two binary integers together (up to 8 bits) and explain overflow errors → Students must understand binary addition and overflow conditions.
- Understand the terms ‘most significant bit’ and ‘least significant bit’ → Supports deeper understanding of binary structure relevant to addition.
Data and Computational Thinking:
- Data representation and manipulation → Binary addition supports understanding of how data is stored and processed digitally.
- 1.5 Computational Thinker → Students develop and apply strategies for understanding and solving problems using binary arithmetic.
- 1.4 Innovative Designer → Binary addition can be part of designing computational solutions involving numeric data.
Algorithms and Programming (AP):
- 2-AP-11: Create programs that use variables to store and modify data → Binary addition exercises often involve manipulating binary values in code.
Data and Analysis (DA):
- 2-DA-07: Represent data in multiple ways → Binary addition helps students understand numeric data representation and transformation.
- MS-ETS1-1: Define criteria and constraints of a design problem → Binary operations can be part of computational design challenges.
- Science Practices: Using mathematics and computational thinking → Binary addition is a direct application of computational thinking in digital systems.
- CCSS.MATH.CONTENT.6.EE.A.2: Write, read, and evaluate expressions in which letters stand for numbers → Binary addition supports understanding of numeric expressions and symbolic reasoning.
- CCSS.MATH.CONTENT.7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers → Binary arithmetic introduces students to alternative number systems and problem-solving strategies.
Lesson: Theory (Binary Addition)
Starter
Option 1: Binary Match-Up Challenge (5–10 mins)
Objective: Reinforce understanding of binary representation of decimal numbers.
How it works:
Starter
Option 1: Binary Match-Up Challenge (5–10 mins)
Objective: Reinforce understanding of binary representation of decimal numbers.
How it works:
- Prepare a set of cards: half with decimal numbers (e.g., 1–15), and half with their binary equivalents.
- Hand out one card to each student.
- Students must walk around and find their matching pair. Once they find a match, the students must sit next to each other an put up their hands.
Option 2: Kahoot quiz (5-10 mins)
Create a 'binary-to-decimal' Kahoot quiz (https://kahoot.com/) with 8-10 questions.
Example Question:
What is 0001 in decimal?
A) 1 ✅
B) 2
C) 3
D) 0
Create a 'binary-to-decimal' Kahoot quiz (https://kahoot.com/) with 8-10 questions.
Example Question:
What is 0001 in decimal?
A) 1 ✅
B) 2
C) 3
D) 0
Option 3: Binary Bingo
How to Play:
Tools for Random Number Generation:
How to Play:
- Hand out the pre-prepared bingo cards (one to each student)
Top tip: Laminate each card so you can use them again. - Call out denary numbers:
- Use a random number generator to pick numbers between 0 and 15.
- Students must match the denary number to the binary numbers on their card.
- Winning the game:
- First to complete a row, column, or diagonal shouts “Binary Bingo!”
- You can verify their answers by asking them to explain a few conversions.
Tools for Random Number Generation:
- Online Generator: https://www.random.org/ or Google “random number between 0 and 15”.
- Custom: Create a simple script that picks a random number between 0 and 15 using Scratch or Python (See example below).
| idea_66_binary_bingo_cards.pdf |
Simple binary bingo caller (Python)
Introduction (Theory)
Begin by writing a simple sum (adding to denary numbers together) on the board:
Begin by writing a simple sum (adding to denary numbers together) on the board:
Ask for a volunteer to solve it (showing all working out).
Explain that, when two numbers are added together in denary (decimal), the first number is combined with the second number to produce a sum. For example, 1 + 2 = 3. Share the following example or write the example on the board.
Explain that, when two numbers are added together in denary (decimal), the first number is combined with the second number to produce a sum. For example, 1 + 2 = 3. Share the following example or write the example on the board.
Next, introduce a simple binary sum:
Explain that, in binary addition, different rules are applied. Inform the students that there are four basic rules for adding two binary numbers:
Example – adding 01 + 10
1 + 0 = 1
0 + 1 = 1
Result in binary: 11 (which represents denary 3)
- 0 + 0 = 0
- 1 + 0 = 1
- 1 + 1 = 10 (binary equivalent of denary 2)
- 1 + 1 + 1 = 11 (binary equivalent of denary 3)
Example – adding 01 + 10
1 + 0 = 1
0 + 1 = 1
Result in binary: 11 (which represents denary 3)
Explain that adding binary numbers is similar to adding denary numbers however, instead of carrying groups of ten, you carry groups of 2.
Example – adding 01 + 01
1 + 1 = 0, carry 1
0 + 0 + 1 = 1
Result in binary: 10 (which represents denary 2)
Share the example below, or write the example on the board, and explain that, when we add two 1s, we need to carry over to the next column.
Example – adding 01 + 01
1 + 1 = 0, carry 1
0 + 0 + 1 = 1
Result in binary: 10 (which represents denary 2)
Share the example below, or write the example on the board, and explain that, when we add two 1s, we need to carry over to the next column.
Follow this by writing the following example on the board and asking students to work it out (showing their working out):
Finally, write the following binary sum on the board and ask the students to solve it. Ask students to identify the problem.
Overflow
Explain that, if we only have 4 bits to store the result, there would be no room for the final carry – resulting in the wrong answer. Explain that when there isn’t room to store the resulting calculation, we get an error which we call overflow
Checking answers
Explain to students that they can check their answers by converting each binary number into denary (decimal) and checking the calculation. Share the following example.
Example:
1101 (binary) = 13 (denary)
0101 (binary) = 5 (denary)
Binary addition: 1101 + 0101 = 10010
Denary check: 13 + 5 = 18. The binary result 10010 is also 18.
Explain that, if we only have 4 bits to store the result, there would be no room for the final carry – resulting in the wrong answer. Explain that when there isn’t room to store the resulting calculation, we get an error which we call overflow
Checking answers
Explain to students that they can check their answers by converting each binary number into denary (decimal) and checking the calculation. Share the following example.
Example:
1101 (binary) = 13 (denary)
0101 (binary) = 5 (denary)
Binary addition: 1101 + 0101 = 10010
Denary check: 13 + 5 = 18. The binary result 10010 is also 18.
Main activity
Option 1 (Unplugged): Binary addition challenges
Hand out the following worksheet, containing a series of binary addition questions, and challenge students to solve them all.
Option 1 (Unplugged): Binary addition challenges
Hand out the following worksheet, containing a series of binary addition questions, and challenge students to solve them all.
| binary_addition_questions.pdf |
Binary addition (student worksheet)
| binary_addition_solution.pdf |
Binary addition (teacher solution)
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Option 2 (Digital): Binary Blast Off Game
Direct student to 'Binary Blast Off'. Link: teachwithict.com/binary_blast_off.html Explain to students that their mission is to fuel their spaceship by solving binary addition problems. Each correct calculation powers up the fuel cells. Challenge students to see who can get the highest score or longest streak of correct answers. |
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Extension task
Challenge students to create their own binary addition puzzles to share with their partner.
Challenge students to create their own binary addition puzzles to share with their partner.
Plenary
Option 1: Exit ticket
Ask students to complete the following statement:
“Today I learned ______________. One challenge I faced was ______________. Next time, I want to try ______________.”
Option 2: Binary Blast Off
Option 1: Exit ticket
Ask students to complete the following statement:
“Today I learned ______________. One challenge I faced was ______________. Next time, I want to try ______________.”
Option 2: Binary Blast Off
- Launch the Game: Open Binary Blast Off on the main screen or board (teachwithict.com/binary_blast_off.html)
- Start the Challenge: Click Start to reveal the first binary addition puzzle.
- Select a Student: Choose a student at random—use a name picker if you like—and invite them to the board to solve the puzzle.
- Pass the Baton: If they solve it correctly, they get to pick the next classmate to tackle the following puzzle.
Tags: GCSE, KS4, Theory, Computing Theory, CS Theory, Binary, Binary Representation, binary 2, binary conversion, how to do binary conversion, counting binary, binary number to decimal, binary 101, 8 binary, binary digits, binary digit, meaning of binary
