← ACARA Digital Technologies Years 5–6

A binary alphabet with two symbols

A key that lets two different symbols, like A and B, stand for the binary values 0 and 1. Any two symbols work if each one always keeps the same meaning.

Part of: ACARA Digital Technologies Years 5–6 — Representing Data with Numbers — Module 7

Understanding A binary alphabet with two symbols in ACARA Digital Technologies Years 5–6

What it does: X and O are two different symbols, so they can be a binary alphabet just like 0 and 1. All three show the same message. With A = 0 and B = 1, or O = 0 and X = 1, the pattern stays the same. A is 0 and B is 1, so A B B A becomes 0 1 1 0. 1 is O and 0 is X, so 1 0 1 0 becomes O X O X. A key only works if each symbol always means the same thing. Otherwise nobody can decode the message. In Key 2, A is 1 and B is 0, so A A B becomes 1 1 0. Swapping the symbols changes the numbers.

Common mistakes: The key is swapped, so ABBA would be 1001, not 0110. With A = 0 and B = 1 the message ABBA matches 0110, so the line should be Key: A = 0, B = 1. X = 0 and O = 1, so XXOX is 0, 0, 1, 0. The binary line should be 0010, not 0100.

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This module's key terms are also in a printable crossword (Modules 44–57) and word search (Modules 44–71).

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Learning
Duo
Which statement is true about a binary alphabet?
Only the digits 0 and 1 can ever be used.Any two different symbols can stand for 0 and 1.
Matches
A = 0, A = 1
↓
The same symbol is used for both 0 and 1, so you cannot tell which value it means. Each value needs its own symbol, like A = 0 and B = 1.
Applying
Meanings
Term
A = 0, B = 1
Meaning
A key that lets two different symbols, like A and B, stand for the binary values 0 and 1. Any two symbols work if each one always keeps the same meaning.
Practice
A = 0
Testing
Gaps
Binary: 110
Check Answer
Spots
1Key: A = 0, B = 1
2Key: A = 1, B = 0

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Quick Questions

1. Which statement is true about a binary alphabet?
A. Only the digits 0 and 1 can ever be used.
B. Any two different symbols can stand for 0 and 1. ✓
Binary only needs two different symbols. They can be 0 and 1, A and B, or X and O.
2. If A = 0 and B = 1, what does the message ABBA mean in 0s and 1s?
A. 0110 ✓
B. 1001
A is 0 and B is 1, so A B B A becomes 0 1 1 0.
3. If X = 0 and O = 1, which message is the same as 1010?
A. XOXO
B. OXOX ✓
1 is O and 0 is X, so 1 0 1 0 becomes O X O X.
4. Mia writes A = 0 and B = 1. Later she uses A to mean 1. Is this a good key?
A. No, each symbol must always keep the same meaning. ✓
B. Yes, a symbol can change meaning whenever you like.
A key only works if each symbol always means the same thing. Otherwise nobody can decode the message.
5. Key 1: A = 0, B = 1. Key 2: A = 1, B = 0. What does the message AAB mean using Key 2?
A. 110 ✓
B. 001
In Key 2, A is 1 and B is 0, so A A B becomes 1 1 0. Swapping the symbols changes the numbers.

Match the Pairs

A = 0, B = 1 → A key that says the letter A stands for 0 and the letter B stands for 1
ABBA → The binary message 0110 when A = 0 and B = 1
Any two different symbols can stand for 0 and 1, such as X and O → X = 1, O = 0
The same message can be written with different symbols if the key changes → 0110 = ABBA = OXXO
A = 0, A = 1 → The same symbol is used for both 0 and 1, so you cannot tell which value it means. Each value needs its own symbol, like A = 0 and B = 1.
Key: A = 0, B = 1. Message: ABBA decoded as 0100 → The last A was decoded as 0 in one place but the second B was decoded as 0. B always means 1, so ABBA is 0110.

Key Term

A = 0, B = 1
A key that lets two different symbols, like A and B, stand for the binary values 0 and 1. Any two symbols work if each one always keeps the same meaning.

Fill in the Blanks

1. Key: A = 0, B = 1 Message: ABBA Binary: 0110
Hint: Type the binary digit that the first letter of the message stands for.
2. Key: X = 1, O = 0 Binary: 1001 Message: XOOX
Hint: Type the symbol that stands for the second binary digit.
3. Key: A = 0, B = 1 Binary: 0011 Message: AABB
Hint: Type the letter that stands for the third binary digit.
4. Message: ABAB Key 1: A = 0, B = 1 -> 0101 Key 2: A = 1, B = 0 -> 1010
Hint: Type the binary digit that the second letter stands for when the key is swapped.
5. Key: X = 0, O = 1 Message: XOOX Binary: 0110
Hint: Type the binary digit that matches the third symbol in the message.

Spot the Error

Question 1
A Key: A = 0, B = 1
B Key: A = 1, B = 0
C Binary: 0110
Line B — The key is swapped, so ABBA would be 1001, not 0110. With A = 0 and B = 1 the message ABBA matches 0110, so the line should be Key: A = 0, B = 1.
Question 2
A Key: X = 0, O = 1
B Message: XXOX
C Binary: 0100
Line C — X = 0 and O = 1, so XXOX is 0, 0, 1, 0. The binary line should be 0010, not 0100.
Question 3
A Key: Y = 0, Y = 1
B Message: NNYN
C Binary: 1101
Line A — A binary alphabet needs two different symbols. Using Y for both 0 and 1 makes it impossible to decode. It should be Key: Y = 0, N = 1.
Question 4
A Key: A = 0, B = 1
B Binary: 1001
C Message: BABA
Line C — The binary 1001 is 1, 0, 0, 1, which is B, A, A, B. The message should be BAAB, not BABA.
Question 5
A Key: # = 0, * = 1
B Message: **##*
C Binary: 11010
Line B — The binary 11010 uses * for 1 and # for 0, giving **#*#. The broken line has the wrong order, so it should be Message: **#*#.

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