More colours need more binary digits

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Quick Questions

Shade in the A or B circle for each question.

1. How many colours can one pixel show if it uses 1 bit?

A 1 colour

B 2 colours

2. How many colours can a pixel show with 2 bits?

A 4 colours

B 3 colours

3. Which list shows EVERY code for 2 bits?

A 00, 01, 10, 11

B 00, 01, 11

4. When we add one more bit, what happens to the number of colours?

A It goes up by 1

B It doubles

5. How many different codes can 3 bits make?

A 8 codes

B 6 codes

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
12^3		A000, 001, 010, 011, 100, 101, 110, 111
200, 01, 10, 11		B2^1 = 2, 2^2 = 4, 2^3 = 8
3Adding one more bit doubles the number of colours a pixel can show		C2 x 2 is 4, not 2. Two bits give 4 colours, not 2.
4The 3-bit codes include every pattern from the smallest to the largest		DThe list stops halfway. 3 bits have 8 codes, so 100 to 111 are missing.
52 bits can show 2 x 2 = 2 colours		EWith 3 bits a pixel can show 8 different colours
63 bits: 000, 001, 010, 011 (4 colours)		FEvery possible code for 2 bits, giving 4 colours

Definitions

2^bits

Fill in the Blanks

Complete each line of code by filling in the missing parts.

colours = 2 _ bits

colours = 2 ^ ____

2 bits: 00, 01, 10, __

000 001 010 011 100 ___ 110 111

3 bits: 2 * 2 * 2 = _ colours

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A bits = 3

B colours = 2 * bits

C print(colours)

Question 2

A one_bit = ["0", "1", "2"]

B print(len(one_bit))

C print("2 colours")

Question 3

A two_bits = ["00", "01"]

B two_bits += ["10", "12"]

C print(len(two_bits))

Question 4

A colours = 2

B colours = colours * 2

C colours = colours + 2

D print(colours)

Question 5

A def colours(bits)

B return 2 ** bits

C print(colours(3))

Answer Key

More colours need more binary digits

Section A: Quick Questions

B — 2 colours

A — 4 colours

A — 00, 01, 10, 11

B — It doubles

A — 8 codes

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

colours = 2 ^ bits

2 bits: 00, 01, 10, 11

000 001 010 011 100 101 110 111

3 bits: 2 * 2 * 2 = 8 colours

Section E: Spot the Error

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.

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.

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.

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.

A — A function definition must end with a colon. It should be def colours(bits):