Converting hexadecimal to denary
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. What is the hex number 2F as a denary number?
2. Which column values are used from right to left in a hex number?
3. Before multiplying by the column value, what denary value does the hex digit C become?
4. What is the hex number 1A3 in denary?
5. Which working correctly converts the hex number 3E to denary?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 12F = 2 x 16 + 15 | AThe 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. | |
| 21A3 = 1 x 256 + 10 x 16 + 3 | BHex 2F is 47 in denary: the 2 is worth 16 and F is converted to 15 before adding | |
| 3The leftmost digit of a four-digit hex number is multiplied by its column value of 4096 | CB4 = 11 x 16 + 4 = 180 | |
| 4Letters A-F are converted to the values 10-15 before multiplying by the column value | DThe 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. | |
| 53C = 3 x 16 + 12 x 16 = 240 | E3000 = 3 x 4096 = 12288 | |
| 6A1 = 10 x 1 + 1 x 16 = 26 | FHex 1A3 is 419 in denary: A becomes 10, then each digit is multiplied by 256, 16 or 1 and the results are added |
C
Definitions
hex to denary
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
2F = 2 x __ + 15 = 47
2.
2F = 2 x 16 + __ = 47
3.
1A3 = 1 x 256 + __ x 16 + 3 = 419
4.
Column values: 1, 16, 256, ____
5.
B4 = 11 x 16 + 4 x 1 = ___
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
Hex 2F: columns are 10 and 1
B
F = 15
C
2 x 16 = 32
D
32 + 15 = 47
Question 2
A
Convert 3C to denary
B
C = 12
C
3 x 16 = 48
D
48 + 12 = 56
Question 3
A
Convert B5 to denary
B
B = 11
C
11 x 16 = 176
D
176 - 5 = 171
Question 4
A
Convert 1E to denary
B
E = 15
C
1 x 16 = 16
D
16 + 14 = 30
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
Answer Key
Converting hexadecimal to denary
Section A: Quick Questions
Q1
A — 2 x 16 + 15 = 47
Q2
A — 1, 16, 256, 4096
Q3
B — 12
Q4
B — 1 x 256 + 10 x 16 + 3 = 419
Q5
A — 3 x 16 + 14 = 62
Section B: Match the Pairs
Q1
2F = 2 x 16 + 15 → Hex 2F is 47 in denary: the 2 is worth 16 and F is converted to 15 before adding
Q2
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
Q3
The leftmost digit of a four-digit hex number is multiplied by its column value of 4096 → 3000 = 3 x 4096 = 12288
Q4
Letters A-F are converted to the values 10-15 before multiplying by the column value → B4 = 11 x 16 + 4 = 180
Q5
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.
Q6
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.
Section C: Definitions
Q1
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.Section D: Fill in the Blanks
Q1
2F = 2 x 16 + 15 = 47Q2
2F = 2 x 16 + 15 = 47Q3
1A3 = 1 x 256 + 10 x 16 + 3 = 419Q4
Column values: 1, 16, 256, 4096Q5
B4 = 11 x 16 + 4 x 1 = 180Section E: Spot the Error
Q1
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.
Q2
D — 48 + 12 = 60, not 56. The final denary answer for 3C is 60.
Q3
D — The column results must be added, not subtracted. The line should be 176 + 5 = 181.
Q4
B — The letter E has the value 14. F is 15. The line should be E = 14.
Q5
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.