Lesson 3: Binary Bracelets

Big idea: Every piece of information inside a computer — every letter, number, photo, and song — is stored as a long string of 0s and 1s called binary. Today you'll learn to read and write binary, and encode your own initials as a bracelet you can wear.

Part 1 — Binary Place Values

In decimal (our normal number system), each column is worth 10 times the column to its right:

  Thousands | Hundreds | Tens | Ones
    1,000   |   100    |  10  |  1

In binary, each column is worth 2 times the column to its right:

  128 | 64 | 32 | 16 | 8 | 4 | 2 | 1

To find the decimal value of a binary number, multiply each digit by its column value and add them all up.

Worked example — Binary to Decimal:

Binary number:   0  1  0  0  0  0  0  1
Column values: 128 64 32 16  8  4  2  1

Calculation: (0×128) + (1×64) + (0×32) + (0×16) + (0×8) + (0×4) + (0×2) + (1×1)
           =    0   +   64   +    0   +    0   +   0  +   0  +   0  +   1
           = 65

So binary 01000001 = decimal 65

Worked example — Decimal to Binary:

Convert decimal 72 to binary.

Step 1: Is 128 ≤ 72?  NO  → write 0.  Remaining: 72
Step 2: Is  64 ≤ 72?  YES → write 1.  Remaining: 72 - 64 = 8
Step 3: Is  32 ≤  8?  NO  → write 0.  Remaining: 8
Step 4: Is  16 ≤  8?  NO  → write 0.  Remaining: 8
Step 5: Is   8 ≤  8?  YES → write 1.  Remaining: 8 - 8  = 0
Step 6: Is   4 ≤  0?  NO  → write 0.  Remaining: 0
Step 7: Is   2 ≤  0?  NO  → write 0.  Remaining: 0
Step 8: Is   1 ≤  0?  NO  → write 0.  Remaining: 0

Result: 0 1 0 0 1 0 0 0  →  01001000

So decimal 72 = binary 01001000. (72 is the ASCII code for the letter H.)

Part 2 — Conversion Practice

Section A — Binary to Decimal

Use the place value table to convert each binary number to decimal.

Place values: 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1

1. Binary: 0 0 1 1 0 0 1 0

  128  64  32  16   8   4   2   1
    0   0   _   _   0   0   _   0

2. Binary: 0 1 0 0 0 0 1 1

  128  64  32  16   8   4   2   1
    0   _   0   0   0   0   _   _

3. Binary: 0 1 1 0 0 0 0 1

  128  64  32  16   8   4   2   1
    0   _   _   0   0   0   0   _

Section B — Decimal to Binary

Convert each decimal number to 8-bit binary. Fill in the grid — write 1 if you used that column, 0 if you didn't.

4. Decimal: 66

  128 |  64 |  32 |  16 |   8 |   4 |   2 |   1
  ___ | ___ | ___ | ___ | ___ | ___ | ___ | ___

Show your working:

64 used? ___  Remainder: ___
32 used? ___  Remainder: ___
16 used? ___  Remainder: ___
 8 used? ___  Remainder: ___
 4 used? ___  Remainder: ___
 2 used? ___  Remainder: ___
 1 used? ___

5. Decimal: 77

  128 |  64 |  32 |  16 |   8 |   4 |   2 |   1
  ___ | ___ | ___ | ___ | ___ | ___ | ___ | ___

6. Decimal: 83

  128 |  64 |  32 |  16 |   8 |   4 |   2 |   1
  ___ | ___ | ___ | ___ | ___ | ___ | ___ | ___

Part 3 — ASCII Table

ASCII (American Standard Code for Information Interchange) is the agreed standard that says which number represents which character. Here are the letters you'll need:

Uppercase Letters (A–Z): ASCII values 65–90

Lowercase Letters (a–z): ASCII values 97–122

Quick check: Notice that uppercase 'A' = 65 and lowercase 'a' = 97. The difference is 32. Can you see which single bit changes? Compare 01000001 (A) and 01100001 (a) — it's bit 6 (the 32-column)!

Part 4 — Bracelet Planning Grid

Step 1: Choose up to 5 letters (eg: your name, or your initials).

Step 2: Look up each letter in the ASCII table and find its binary representation.

Step 3: Fill in the planning grid — shade or colour in each square where the bit is 1. Leave blank (or write 0) for bits that are 0.

Step 4: Use your grid as a blueprint for stringing beads.

Bead key:

• White bead \= 0 (unshaded)
• Dark bead \= 1 (shaded)
• Red bead (×3) \= separator between letters

Planning Grid

Letter 1: _____   (ASCII decimal: _____)

  Bit:   128 | 64 | 32 | 16 |  8 |  4 |  2 |  1
  -----+-----+----+----+----+----+----+----+----+
  0/1? |     |    |    |    |    |    |    |    |
  -----+-----+----+----+----+----+----+----+----+
  Bead:|     |    |    |    |    |    |    |    |
       | (W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|

Letter 2: _____   (ASCII decimal: _____)

  Bit:   128 | 64 | 32 | 16 |  8 |  4 |  2 |  1
  -----+-----+----+----+----+----+----+----+----+
  0/1? |     |    |    |    |    |    |    |    |
  -----+-----+----+----+----+----+----+----+----+
  Bead:|     |    |    |    |    |    |    |    |
       | (W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|

Letter 3: _____   (ASCII decimal: _____)

  Bit:   128 | 64 | 32 | 16 |  8 |  4 |  2 |  1
  -----+-----+----+----+----+----+----+----+----+
  0/1? |     |    |    |    |    |    |    |    |
  -----+-----+----+----+----+----+----+----+----+
  Bead:|     |    |    |    |    |    |    |    |
       | (W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|

Letter 4: _____   (ASCII decimal: _____)

  Bit:   128 | 64 | 32 | 16 |  8 |  4 |  2 |  1
  -----+-----+----+----+----+----+----+----+----+
  0/1? |     |    |    |    |    |    |    |    |
  -----+-----+----+----+----+----+----+----+----+
  Bead:|     |    |    |    |    |    |    |    |
       | (W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|

Letter 5: _____   (ASCII decimal: _____)

  Bit:   128 | 64 | 32 | 16 |  8 |  4 |  2 |  1
  -----+-----+----+----+----+----+----+----+----+
  0/1? |     |    |    |    |    |    |    |    |
  -----+-----+----+----+----+----+----+----+----+
  Bead:|     |    |    |    |    |    |    |    |
       | (W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|(W/D)|

Part 5 — Bracelet Instructions

1. Tie a knot at one end of your elastic cord, leaving a 3 cm tail.
2. Thread beads in order from your planning grid, left column to right.
3. After each letter's 8 beads, thread 3 red separator beads.
4. When all letters are done, add enough white (0) beads to comfortably wrap your wrist.
5. Thread the elastic back through the first 2–3 beads to create a loop, then tie a double knot tightly. Trim the extra cord.

Stringing tip: Go slowly. Tick off each bead in your grid as you thread it. If you lose count, stop and recount from the last separator.

Reflection Questions

1. How many different values can 1 bit (one switch) represent? How many can 8 bits represent?

2. What is ASCII? Why do all computers need to use the same code?

3. What does the word binary mean? (Hint: think of what "bi" means in other words like bicycle, bilingual, binoculars...)

4. Look at your bracelet. If someone else can read binary and knows you encoded letters, what do they need to know to decode your bracelet?

5. A photo on a phone takes up about 3 megabytes. 1 megabyte \= 1,000,000 bytes. 1 byte \= 8 bits. How many bits are in one photo?

Extension Challenges

A. Can you decode this mystery binary sequence? (Each group of 8 bits is one letter — use the ASCII table.)

01001000  01000101  01001100  01001100  01001111

B. Uppercase 'A' is 65 (binary: 01000001). Lowercase 'a' is 97 (binary: 01100001). The difference is 32. What is the difference in binary? Which single bit changes between uppercase and lowercase letters?

C. A Year 7 essay might be 500 words with an average of 5 letters per word. Estimate:

• How many characters? _______
• How many bytes? _______
• How many bits? _______

D. ASCII can only represent 128 characters (or 256 in extended ASCII). What problem does this cause for people who write in Japanese, Chinese, Arabic, or Hindi? What do you think was invented to solve this problem?