← ACARA Digital Technologies Years 5–6

More colours need more binary digits

Each extra bit doubles the colours a pixel can show: 1 bit gives 2, 2 bits give 4 and 3 bits give 8. So the number of colours is 2 times itself, once for each bit.

Part of: ACARA Digital Technologies Years 5–6 — Representing Data with Numbers — Module 19, ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 30

Understanding More colours need more binary digits in ACARA Digital Technologies Years 5–6

What it does: Each time the bit count goes up by 1, the number of colours is multiplied by 2: 2, 4, then 8. There are 8 codes of 3 bits, one for each of the 8 colours a pixel can show. 1 bit can be 0 or 1, so it gives 2 different codes. That means 2 colours. The list must have 4 codes. 10 is missing from the wrong list. 2 x 2 x 2 = 8. The codes run from 000 to 111. Binary codes only use the digits 0 and 1. A 3-bit code has exactly 3 digits.

Common mistakes: The number of colours is 2 multiplied by itself once for each bit, so it needs 2 ** bits. 2 * bits gives 6 for 3 bits, but 3 bits really give 8 colours. A bit can only be 0 or 1, so one bit gives just 2 codes. The list should be ["0", "1"]. There is no digit 2 in binary.

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Learning
Duo
How many colours can one pixel show if it uses 1 bit?
2 colours1 colour
Matches
2 bits can show 2 x 2 = 2 colours
↓
2 x 2 is 4, not 2. Two bits give 4 colours, not 2.
Applying
Meanings
Term
2^bits
Meaning
Each extra bit doubles the colours a pixel can show: 1 bit gives 2, 2 bits give 4 and 3 bits give 8. So the number of colours is 2 times itself, once for each bit.
Practice
1 bit: 2^1 = 2 colours
Testing
Gaps
colours = 2 bits
Check Answer
Spots
1bits = 3
2colours = 2 * bits

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Quick Questions

1. How many colours can one pixel show if it uses 1 bit?
A. 1 colour
B. 2 colours ✓
1 bit can be 0 or 1, so it gives 2 different codes. That means 2 colours.
2. How many colours can a pixel show with 2 bits?
A. 4 colours ✓
B. 3 colours
The codes are 00, 01, 10 and 11. That is 4 codes, so 4 colours.
3. Which list shows EVERY code for 2 bits?
A. 00, 01, 10, 11 ✓
B. 00, 01, 11
The list must have 4 codes. 10 is missing from the wrong list.
4. When we add one more bit, what happens to the number of colours?
A. It goes up by 1
B. It doubles ✓
Each extra bit doubles the colours: 2, then 4, then 8, then 16.
5. How many different codes can 3 bits make?
A. 8 codes ✓
B. 6 codes
2 x 2 x 2 = 8. The codes run from 000 to 111.

Match the Pairs

2^3 → With 3 bits a pixel can show 8 different colours
00, 01, 10, 11 → Every possible code for 2 bits, giving 4 colours
Adding one more bit doubles the number of colours a pixel can show → 2^1 = 2, 2^2 = 4, 2^3 = 8
The 3-bit codes include every pattern from the smallest to the largest → 000, 001, 010, 011, 100, 101, 110, 111
2 bits can show 2 x 2 = 2 colours → 2 x 2 is 4, not 2. Two bits give 4 colours, not 2.
3 bits: 000, 001, 010, 011 (4 colours) → The list stops halfway. 3 bits have 8 codes, so 100 to 111 are missing.

Key Term

2^bits
Each extra bit doubles the colours a pixel can show: 1 bit gives 2, 2 bits give 4 and 3 bits give 8. So the number of colours is 2 times itself, once for each bit.

Fill in the Blanks

1. colours = 2 ^ bits
Hint: Type the symbol that means 'to the power of' in the colour rule.
2. colours = 2 ^ bits
Hint: Type the word for the thing that is added to make more colours.
3. 2 bits: 00, 01, 10, 11
Hint: Type the last code in the list of every 2-bit code.
4. 000 001 010 011 100 101 110 111
Hint: Type the missing 3-bit code that fits in the counting order.
5. 3 bits: 2 * 2 * 2 = 8 colours
Hint: Type the total number of colours that 3 bits can show.

Spot the Error

Question 1
A bits = 3
B colours = 2 * bits
C print(colours)
Line B — The number of colours is 2 multiplied by itself once for each bit, so it needs 2 ** bits. 2 * bits gives 6 for 3 bits, but 3 bits really give 8 colours.
Question 2
A one_bit = ["0", "1", "2"]
B print(len(one_bit))
C print("2 colours")
Line A — A bit can only be 0 or 1, so one bit gives just 2 codes. The list should be ["0", "1"]. There is no digit 2 in binary.
Question 3
A two_bits = ["00", "01"]
B two_bits += ["10", "12"]
C print(len(two_bits))
Line B — Binary codes only use the digits 0 and 1. The last 2-bit code should be "11", not "12". The four codes are 00, 01, 10 and 11.
Question 4
A colours = 2
B colours = colours * 2
C colours = colours + 2
D print(colours)
Line C — Each extra bit doubles the number of colours, so the line should multiply by 2. Adding 2 gives 6 instead of 8 colours for 3 bits.
Question 5
A def colours(bits)
B return 2 ** bits
C print(colours(3))
Line A — A function definition must end with a colon. It should be def colours(bits):

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