← IGCSE Computer Science Paper 1

Converting hexadecimal to denary

Multiply each hex digit's value (A-F = 10-15) by its column value (1, 16, 256, 4096), then add the results. Example: 2F = 2 x 16 + 15 = 47.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 15

Understanding Converting hexadecimal to denary in IGCSE Computer Science Paper 1

What it does: In a four-digit hex number the columns are 4096, 256, 16 and 1, so a 3 in the first column is worth 3 x 4096 = 12288. B is worth 11, so the 16s column gives 11 x 16 = 176. Adding the 4 gives 180. The 2 is in the 16s column, so it is worth 2 x 16 = 32. F is 15 in the 1s column. 32 + 15 = 47. Hexadecimal is base 16, so each column is worth 16 times the one to its right. Denary uses 10s, 100s and 1000s. A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. Convert the letter to its number first.

Common mistakes: Hex column values are powers of 16, so a two-digit number uses 16 and 1, not 10 and 1. The line should say 16 and 1. 48 + 12 = 60, not 56. The final denary answer for 3C is 60.

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Learning
Duo
What is the hex number 2F as a denary number?
2 x 16 + 15 = 472 + 15 = 17
Matches
3C = 3 x 16 + 12 x 16 = 240
↓
The right-hand digit was multiplied by 16 instead of 1. The units column is worth 1, so the answer should be 3 x 16 + 12 x 1 = 60.
Applying
Meanings
Term
hex to denary
Meaning
Multiply each hex digit's value (A-F = 10-15) by its column value (1, 16, 256, 4096), then add the results. Example: 2F = 2 x 16 + 15 = 47.
Practice
2F: F = 15
Testing
Gaps
2F = 2 x + 15 = 47
Check Answer
Spots
1Hex 2F: columns are 10 and 1
2F = 15

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Quick Questions

1. What is the hex number 2F as a denary number?
A. 2 x 16 + 15 = 47 ✓
B. 2 + 15 = 17
The 2 is in the 16s column, so it is worth 2 x 16 = 32. F is 15 in the 1s column. 32 + 15 = 47.
2. Which column values are used from right to left in a hex number?
A. 1, 16, 256, 4096 ✓
B. 1, 10, 100, 1000
Hexadecimal is base 16, so each column is worth 16 times the one to its right. Denary uses 10s, 100s and 1000s.
3. Before multiplying by the column value, what denary value does the hex digit C become?
A. 13
B. 12 ✓
A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. Convert the letter to its number first.
4. What is the hex number 1A3 in denary?
A. 1 x 256 + 10 + 3 = 269
B. 1 x 256 + 10 x 16 + 3 = 419 ✓
The A is in the 16s column, so it must be multiplied by 16: 10 x 16 = 160. Then 256 + 160 + 3 = 419.
5. Which working correctly converts the hex number 3E to denary?
A. 3 x 16 + 14 = 62 ✓
B. 3 x 14 + 16 = 58
The column value (16) multiplies the 3. The letter E becomes 14 and is added in the 1s column. 48 + 14 = 62.

Match the Pairs

2F = 2 x 16 + 15 → Hex 2F is 47 in denary: the 2 is worth 16 and F is converted to 15 before adding
1A3 = 1 x 256 + 10 x 16 + 3 → Hex 1A3 is 419 in denary: A becomes 10, then each digit is multiplied by 256, 16 or 1 and the results are added
The leftmost digit of a four-digit hex number is multiplied by its column value of 4096 → 3000 = 3 x 4096 = 12288
Letters A-F are converted to the values 10-15 before multiplying by the column value → B4 = 11 x 16 + 4 = 180
3C = 3 x 16 + 12 x 16 = 240 → The right-hand digit was multiplied by 16 instead of 1. The units column is worth 1, so the answer should be 3 x 16 + 12 x 1 = 60.
A1 = 10 x 1 + 1 x 16 = 26 → The column values are the wrong way round. The left digit is worth 16 and the right digit is worth 1, so the answer is 10 x 16 + 1 x 1 = 161.

Key Term

hex to denary
Multiply each hex digit's value (A-F = 10-15) by its column value (1, 16, 256, 4096), then add the results. Example: 2F = 2 x 16 + 15 = 47.

Fill in the Blanks

1. 2F = 2 x 16 + 15 = 47
Hint: Type the column value that the digit 2 is multiplied by (second column from the right).
2. 2F = 2 x 16 + 15 = 47
Hint: Type the denary value of the hex letter F.
3. 1A3 = 1 x 256 + 10 x 16 + 3 = 419
Hint: Type the denary value of the hex letter A before multiplying.
4. Column values: 1, 16, 256, 4096
Hint: Type the column value of the fourth column from the right.
5. B4 = 11 x 16 + 4 x 1 = 180
Hint: Type the denary total after adding the two results together.

Spot the Error

Question 1
A Hex 2F: columns are 10 and 1
B F = 15
C 2 x 16 = 32
D 32 + 15 = 47
Line A — Hex column values are powers of 16, so a two-digit number uses 16 and 1, not 10 and 1. The line should say 16 and 1.
Question 2
A Convert 3C to denary
B C = 12
C 3 x 16 = 48
D 48 + 12 = 56
Line D — 48 + 12 = 60, not 56. The final denary answer for 3C is 60.
Question 3
A Convert B5 to denary
B B = 11
C 11 x 16 = 176
D 176 - 5 = 171
Line D — The column results must be added, not subtracted. The line should be 176 + 5 = 181.
Question 4
A Convert 1E to denary
B E = 15
C 1 x 16 = 16
D 16 + 14 = 30
Line B — The letter E has the value 14. F is 15. The line should be E = 14.
Question 5
A Convert 1A3 to denary
B 1 x 256 = 256
C 10 x 16 = 100
D 3 x 1 = 3
E 256 + 160 + 3 = 419
Line C — 10 x 16 = 160, not 100. A has the value 10 and sits in the 16s column, so the line should be 10 x 16 = 160.

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