← IGCSE Computer Science Paper 1

Hexadecimal place values

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.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 14

Understanding Hexadecimal place values in IGCSE Computer Science Paper 1

What it does: The largest 2-digit hex value F in each column gives 15 x 16 + 15 = 255, which is the top of the range. Four F digits use the columns 4096, 256, 16 and 1 at their maximum, giving 65535. Each hex column is 16 times the one to its right, so 16 x 16 = 256. The biggest column is on the left, so the order is 4096, 256, 16, 1. Hex is base 16, so every column to the left is worth 16 times more. Binary is the one that uses 2 times. 16^0 = 1, 16^1 = 16, 16^2 = 256 and 16^3 = 4096.

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

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Learning

Duo

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

32256

Matches

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.

Applying

Meanings

Term

4096 256 16 1

Meaning

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.

Practice

4096 256 16 1

Testing

Gaps

Hex columns: 256 16 1

Check Answer

Spots

2tens = 2 * 16

3ones = 15 * 16

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Quick Questions

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

A. 32

B. 256 ✓

Each hex column is 16 times the one to its right, so 16 x 16 = 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

The biggest column is on the left, so the order is 4096, 256, 16, 1.

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

A. 16 times ✓

B. 2 times

Hex is base 16, so every column to the left is worth 16 times more. Binary is the one that uses 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)

16^0 = 1, 16^1 = 16, 16^2 = 256 and 16^3 = 4096.

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

A. 0 to 256

B. 0 to 255 ✓

The largest 2-digit hex number is FF = 15 x 16 + 15 = 255.

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.

Key Term

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.

Fill in the Blanks

1. Hex columns: 4096 256 16 1

Hint: Type the place value of the leftmost of the four hex columns.

2. column value = 16 x column on its right

Hint: Type the number you multiply by each time you move one hex column to the left.

3. 16^2 = 256

Hint: Type the denary value of 16 squared, which is the third column from the right.

4. FF = 15 x 16 + 15 = 255

Hint: Type the denary value of the largest 2-digit hex number.

5. 4 hex digits cover 0 to 65535

Hint: Type the largest denary value that four hex digits can store.

Spot the Error

Question 1

A h = '2F'

B tens = 2 * 16

C ones = 15 * 16

D print(tens + ones)

Line 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.

Question 2

A # Hex columns, left to right

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

C print(cols[1] * 16)

Line 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].

Question 3

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

B print(cols[0] // 16)

C print(cols[3] * 16)

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

Question 4

A c0 = 16 ** 0

B c1 = 16 ** 1

C c2 = 16 * 2

D print(c0, c1, c2)

Line 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.

Question 5

A c0 = 1

B c1 = c0 * 16

C c2 = c1 * 16

D c3 = c2 * 10

E print(c3)

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

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