Number of colours from the colour depth

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Quick Questions

Shade in the A or B circle for each question.

1. A colour depth of 2 bits allows how many different colours?

A 4 colours

B 2 colours

2. A colour depth of 8 bits allows how many different colours?

A 64 colours

B 256 colours

3. Which formula gives the number of colours for a colour depth of n bits?

A 2^n

B n^2

4. An image has its colour depth increased from 3 bits to 4 bits. What happens to the number of colours?

A It doubles from 8 to 16

B It goes up by 1 from 8 to 9

5. A colour depth of 1 bit allows 2 colours, for example black and white. True or false: 1 bit can store 1 colour only.

A True: 1 bit gives 1 colour

B False: 1 bit gives 2 colours

Match the Pairs

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

Left column		Right column
1colours = 2^n		AAn 8-bit colour depth allows 256 different colours
22^8 = 256		B2^4 = 2 * 2^3
3A 2-bit colour depth gives 4 different colours		C2^2 = 4
4Adding one extra bit doubles the number of colours (3 bits to 4 bits: 8 to 16 colours)		DThe wrong power was used. The power is the number of bits, so 2 bits give 2^2 = 4 colours.
5colours = 2 * n (n = 8 gives 16 colours)		EThe colours are found by multiplying n by 2, but the correct rule is 2 to the power n. 8 bits give 2^8 = 256 colours, not 16.
62 bits = 2^3 = 8 colours		FA colour depth of n bits gives 2 to the power n different colours

Definitions

colours = 2^n

Fill in the Blanks

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

colours = 2 _ bits

2 bits give 2 ^ 2 = _ colours

8 bits give 2 ^ 8 = ___ colours

bits = bits + 1 colours = colours * _

bits = 4 colours = _ ^ bits print(colours)

Spot the Error

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

Question 1

A depth ← 3

B colours ← 2 ^ depth

C OUTPUT "Colours:"

D OUTPUT depth

Question 2

A colours ← 1

B FOR i ← 1 TO 2

C colours ← colours + 2

D NEXT i

E OUTPUT colours

Question 3

A depth ← 8

B colours ← depth ^ 2

C OUTPUT colours

Question 4

A INPUT colours

B colours ← 2 ^ bits

C OUTPUT colours

Question 5

A old ← 2 ^ 2

B new ← 2 ^ 3

C ratio ← new - old

D OUTPUT ratio

Answer Key

Number of colours from the colour depth

Section A: Quick Questions

A — 4 colours

B — 256 colours

A — 2^n

A — It doubles from 8 to 16

B — False: 1 bit gives 2 colours

Section B: Match the Pairs

colours = 2^n → A colour depth of n bits gives 2 to the power n different colours

2^8 = 256 → An 8-bit colour depth allows 256 different colours

A 2-bit colour depth gives 4 different colours → 2^2 = 4

Adding one extra bit doubles the number of colours (3 bits to 4 bits: 8 to 16 colours) → 2^4 = 2 * 2^3

colours = 2 * n (n = 8 gives 16 colours) → The colours are found by multiplying n by 2, but the correct rule is 2 to the power n. 8 bits give 2^8 = 256 colours, not 16.

2 bits = 2^3 = 8 colours → The wrong power was used. The power is the number of bits, so 2 bits give 2^2 = 4 colours.

Section C: Definitions

colours = 2^n — A colour depth of n bits gives 2^n different colours, so each extra bit doubles the number. For example, 2 bits give 4 colours and 8 bits give 256 colours.

Section D: Fill in the Blanks

colours = 2 ^ bits

2 bits give 2 ^ 2 = 4 colours

8 bits give 2 ^ 8 = 256 colours

bits = bits + 1
colours = colours * 2

bits = 4
colours = 2 ^ bits
print(colours)

Section E: Spot the Error

D — The program should output the number of colours, which is stored in colours. Outputting depth would only show the number of bits (3), not the 8 colours. It should be OUTPUT colours.

C — Each extra bit doubles the number of colours, so the loop must multiply by 2, not add 2. It should be colours ← colours * 2, which gives 4 colours for 2 bits.

B — The formula is 2 to the power of the colour depth, so the base is 2 and the power is the depth. It should be colours ← 2 ^ depth, giving 256, not depth ^ 2, which gives 64.

A — The user should enter the colour depth (bits), which is then used in the calculation. Inputting colours leaves bits with no value. It should be INPUT bits.

C — To show that one extra bit doubles the colours, divide the new number of colours by the old number (8 / 4 = 2). It should be ratio ← new / old, not subtraction.