Binary, Decimal and Hexadecimal

Lesson plan

Level

Beginner

Time

About 50 minutes; the steps below add up to 48

Learners start from what the 3 in 7,302 is worth and work out how to count past 1 with only two digits, so place value and binary come from them. Before each panel or worked example they predict the answer: what 11000000 is worth, how to build 172, and what symbols a sixteen-digit system would use. Checks confirm the 0 to 255 range and why two hex digits make an octet. The habit to build: write the place values above the digits before converting anything.

Objectives

• Explain place value and how the base sets what each position is worth
• Convert between binary and decimal for an octet
• Explain why each part of an IPv4 address lies between 0 and 255
• Read hexadecimal and convert a hex byte to binary and decimal

Before the lesson

• Open this page on your own screen and use “Open the lesson window” to open the lesson in a second window. Share only that second window.
• No prior knowledge beyond whole-number arithmetic.
• Have the octet place values written across the top of the board throughout: 128, 64, 32, 16, 8, 4, 2, 1.
• The lesson takes about 48 minutes.
• In presentation mode every step is shown in turns: Next reveals one moment, part or answer at a time, and the instructor view names what is on screen and what comes next.

Steps

1. Introduction Opening

   On screen: the lesson’s title, module and number; Next adds its objectives and key terms, as the lesson page lists them; Next again begins the first step.

   Objectives on screen

   • Explain place value and how the base sets what each position is worth
   • Convert between binary and decimal for an octet
   • Explain why each part of an IPv4 address lies between 0 and 255
   • Read hexadecimal and convert a hex byte to binary and decimal

   Purpose: Learners start from what the 3 in 7,302 is worth and work out how to count past 1 with only two digits, so place value and binary come from them. Before each panel or worked example they predict the answer: what 11000000 is worth, how to build 172, and what symbols a sixteen-digit system would use. Checks confirm the 0 to 255 range and why two hex digits make an octet. The habit to build: write the place values above the digits before converting anything.

2. 1. What a digit is worth Think 5 min

   Purpose: Find place value from decimal, and invent binary counting.

   Ask

   • How much is the 3 in 7,302 worth?
   • How could you count past 1 with only two digits?

   Responses to expect

   • Counting in binary aloud (0, 1, 10, 11, 100) helps the idea land.
   • On screen in turns: the opening question, its answer; then the question on counting with only two digits, and its answer.

   Discussion pause: Let learners try counting to eight in binary before revealing it.

   In the lesson window

   • Think it through: In the number 7,302, how much is the 3 worth?
   • Think it through: Suppose you could use only two digits, 0 and 1. How could you count past 1?

3. 2. Place value: the idea behind every number system Explain 5 min

   Purpose: Generalise place value to any base, with the comparison table.

   Ask

   • In base 16, what is the third position from the right worth?

   Responses to expect

   • 256.
   • On screen in turns: the opening; then the base, and three systems compared, starting with decimal; binary; hexadecimal.

4. 3. Binary: counting with two digits Experiment 16 min

   Purpose: Read and build octets, and learn the mask values.

   Ask

   • What is 11000000 worth?
   • Why can an address part never be 300?
   • How would you build 172?

   Responses to expect

   • Some read 11000000 as eleven million; point to the base.
   • The mask-octet table holds back its decimal column: let the class add the place values first.
   • On screen in turns: the opening question, its answer; then reading an octet: 11000000 on the panel; why an octet runs from 0 to 255; the check question on 300, and its answer; converting decimal to binary: the question on building 172, and its answer; converting 172, place by place, starting with 128; 64; 32; 16; 8; 4; 2 and 1, and the check; 172 on the panel; values worth knowing: mask octets, with the decimal values held back; the decimal value of each mask octet.

   Misconceptions to challenge

   • A learner may believe: “Binary 10 means ten.” Respond: It means one 2 and no 1s: two.
   • A learner may believe: “An octet can go up to 256.” Respond: It has 256 values, from 0 to 255.

   Discussion pause: In the 172 conversion, reveal one place at a time and let the class say 1 or 0, and what is left, before each appears.

   If the explanation does not land: Use eight learners standing in a row with cards showing 128 to 1; those holding a 1 step forward and the class adds.

   To go further

   • Why are the only values a mask octet can take 0, 128, 192, 224, 240, 248, 252, 254 and 255?

   In the lesson window

   • Think it through: The eight positions of an octet are worth 128, 64, 32, 16, 8, 4, 2 and 1. What do you think 11000000 is worth?
   • Check your understanding: Why can no part of an IPv4 address be 300?
   • Think it through: Before the worked example: how could you decide which bits to set to make 172?

5. 4. Hexadecimal: sixteen digits Predict 10 min

   Purpose: Introduce hexadecimal, its letters, and its link to four bits.

   Ask

   • What symbols could a sixteen-digit system use after 9?
   • How many hex digits make one octet?

   Responses to expect

   • Letters come quickly; the four-bit link is the new idea.
   • On screen in turns: the opening question, its answer; then hexadecimal digits A to F; hex 4A, worked out; why hex suits networking; the check question on hex digits per octet, and its answer; hex digits and their four bits; one byte of a MAC address, starting with splitting it; converting each digit to four bits; joining them; checking in decimal; where you will meet all three systems.

   Misconceptions to challenge

   • A learner may believe: “Hexadecimal letters are case-sensitive.” Respond: 1A and 1a are the same value.

   If the explanation does not land: Group bits in fours like grouping pennies into piles: each pile of four bits is one hex digit, so an octet is two piles.

   In the lesson window

   • Think it through: A number system with sixteen digits needs symbols for ten, eleven, twelve and so on, each written as a single character. What could it use after 9?
   • Check your understanding: How many hexadecimal digits are needed to write one octet?

6. 5. Apply it in a new situation Apply 5 min

   Purpose: Set up independent application, ideally on a later day.

   Ask

   • Who will try these now, and who later in the week?

   Responses to expect

   • Both are calculations; ask learners to show the place values they used.
   • On screen in turns: the opening question, its answer; then the question on hex 3C, and its answer.

   In the lesson window

   • Apply it: What is binary 01100100 in decimal?
   • Apply it: One byte of a MAC address is 3C. What is it in decimal?

7. 6. Check your understanding Check 5 min

   Purpose: Check the lesson against the approved revision-bank questions.

   Ask

   • Answer individually, then compare before revealing.

   Responses to expect

   • Each explanation shows the working; compare it with your own.
   • On screen in turns: the opening; then the revision questions one at a time, each followed by its answer; where to practise next.

8. 7. What to remember Consolidate 2 min

   Purpose: Summarise the five points, the key terms and the misunderstandings.

   Ask

   • Without looking: write the eight octet place values.

   Responses to expect

   • From the left: 128, 64, 32, 16, 8, 4, 2 and 1.
   • On screen in turns: the opening; then the summary; the key terms; the common misunderstandings.

9. Lesson recap Closing

   On screen: the lesson’s objectives again; Next adds the closing question, which asks the class to explain each one in their own words without looking back. It says nothing about what anyone has learnt: use the answers to decide what to revisit.

   Points to listen for

   • Position sets value; the base sets what each position is worth.
   • Add the place values wherever a bit is 1.
   • Eight bits give 0 to 255, and no more.
   • Build binary from the largest place down.
   • Four bits per hex digit, two hex digits per octet.

Consolidation

• Position sets value; the base sets what each position is worth.
• Add the place values wherever a bit is 1.
• Eight bits give 0 to 255, and no more.
• Build binary from the largest place down.
• Four bits per hex digit, two hex digits per octet.