Hexadecimal place values

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Quick Questions

Shade in the A or B circle for each question.

1. What is the value of the column immediately to the left of the 16s column in hexadecimal?

A 32

B 256

2. Which list shows the hex place values from left to right for a 4-digit hex number?

A 4096 256 16 1

B 1 16 256 4096

3. Each hexadecimal column is worth ___ the column to its right.

A 16 times

B 2 times

4. The hex place values are powers of 16. Which power of 16 gives 256?

A 16 squared (16^2)

B 16 cubed (16^3)

5. What is the range of values a 2-digit hex number can store?

A 0 to 256

B 0 to 255

Match the Pairs

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

Left column		Right column
14096 256 16 1		AFFFF = 65535
216 x 16 = 256		BThe place values of a 4-digit hexadecimal number, from left to right
3A 2-digit hex number covers 0 to 255, because FF = 15 x 16 + 15		CThe third column from the right in hex is worth 256, which is 16 squared
4A 4-digit hex number covers 0 to 65535, because FFFF is the largest value		DThese are denary place values (powers of 10). Hex columns go up by 16 each time: 1, 16, 256, 4096.
5Hex place values: 1, 10, 100, 1000		EThe columns are not found by adding 16 or doubling. Each column is multiplied by 16, so the values are 1, 16, 256, 4096.
6Hex place values: 1, 16, 32, 64		FFF = 15 x 16 + 15 = 255

Definitions

4096 256 16 1

Fill in the Blanks

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

Hex columns: ____ 256 16 1

column value = __ x column on its right

16^2 = ___

FF = 15 x 16 + 15 = ___

4 hex digits cover 0 to _____

Spot the Error

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

Question 1

A h = '2F'

B tens = 2 * 16

C ones = 15 * 16

D print(tens + ones)

Question 2

A # Hex columns, left to right

B cols = [4096, 512, 16, 1]

C print(cols[1] * 16)

Question 3

A cols = [1000, 100, 10, 1]

B print(cols[0] // 16)

C print(cols[3] * 16)

Question 4

A c0 = 16 ** 0

B c1 = 16 ** 1

C c2 = 16 * 2

D print(c0, c1, c2)

Question 5

A c0 = 1

B c1 = c0 * 16

C c2 = c1 * 16

D c3 = c2 * 10

E print(c3)

Answer Key

Hexadecimal place values

Section A: Quick Questions

B — 256

A — 4096 256 16 1

A — 16 times

A — 16 squared (16^2)

B — 0 to 255

Section B: Match the Pairs

4096 256 16 1 → The place values of a 4-digit hexadecimal number, from left to right

16 x 16 = 256 → The third column from the right in hex is worth 256, which is 16 squared

A 2-digit hex number covers 0 to 255, because FF = 15 x 16 + 15 → FF = 15 x 16 + 15 = 255

A 4-digit hex number covers 0 to 65535, because FFFF is the largest value → FFFF = 65535

Hex place values: 1, 10, 100, 1000 → These are denary place values (powers of 10). Hex columns go up by 16 each time: 1, 16, 256, 4096.

Hex place values: 1, 16, 32, 64 → The columns are not found by adding 16 or doubling. Each column is multiplied by 16, so the values are 1, 16, 256, 4096.

Section C: Definitions

4096 256 16 1 — Hex place values, left to right. Each column is worth 16 times the column to its right. Two hex digits cover 0 to 255 and four hex digits cover 0 to 65535.

Section D: Fill in the Blanks

Hex columns: 4096 256 16 1

column value = 16 x column on its right

16^2 = 256

FF = 15 x 16 + 15 = 255

4 hex digits cover 0 to 65535

Section E: Spot the Error

C — The right-hand hex column is worth 1, not 16. F (15) in that column is 15 * 1. It should be ones = 15 * 1.

B — Each column is 16 times the one to its right, so the second column is 16 * 16 = 256, not 512. It should be [4096, 256, 16, 1].

A — Those are denary place values (powers of 10). Hex columns are powers of 16, so the list should be [4096, 256, 16, 1].

C — The third hex column is 16 to the power of 2 (16 * 16 = 256). 16 * 2 only gives 32. It should be c2 = 16 ** 2.

D — Each hex column is 16 times the column to its right, not 10 times. c3 should be c2 * 16, which gives 4096.