← IGCSE Computer Science Paper 1

Converting denary to hexadecimal

Divide the denary number by 16 again and again. Read the remainders from last to first, writing 10 to 15 as A to F. Check by converting the hex back to denary.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 16

Understanding Converting denary to hexadecimal in IGCSE Computer Science Paper 1

What it does: The last remainder (12 = C) is written first and the first remainder (8) is written last, giving C8. Multiplying each hex digit by its place value (16 and 1) and adding them should give the original denary number. Hexadecimal is base 16, so you divide by 16 each time. Dividing by 2 is for converting to binary. Remainders 10 to 15 are written as A to F, so 11 becomes B. Writing 11 would look like two separate digits. Keep dividing until the quotient reaches 0. Record the remainder from that last division too. To check, convert back to denary: the 16s digit is multiplied by 16 and A is worth 10. 3 × 16 + 10 = 58, which matches.

Common mistakes: The remainders must be read from last to first, not first to last. The last remainder is 13 (D) and the first is 12 (C), so the answer is DC. 10 is smaller than 16, so 10 / 16 = 0 remainder 10. The line should be 10 / 16 = 0 remainder 10, which gives the digit A.

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This module's key terms are also in a printable crossword (Modules 3–17) and word search (Modules 3–27).

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Learning
Duo
Which number do you repeatedly divide by to convert denary to hexadecimal?
216
Matches
200 = 8C
↓
The remainders were read from first to last instead of last to first. The correct answer is C8.
Applying
Meanings
Term
divide by 16
Meaning
Divide the denary number by 16 again and again. Read the remainders from last to first, writing 10 to 15 as A to F. Check by converting the hex back to denary.
Practice
218 / 16 = 13 remainder 10
Testing
Gaps
200 DIV = 12 remainder 8
Check Answer
Spots
313 / 16 = 0 remainder 13
4Remainders first to last: CD

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Quick Questions

1. Which number do you repeatedly divide by to convert denary to hexadecimal?
A. 16 ✓
B. 2
Hexadecimal is base 16, so you divide by 16 each time. Dividing by 2 is for converting to binary.
2. In what order do you read the remainders to build the hex number?
A. First to last (top to bottom)
B. Last to first (bottom to top) ✓
The last remainder you get is the most significant digit, so it is written first.
3. A remainder of 11 appears during a conversion. How do you write it in the hex answer?
A. B ✓
B. 11
Remainders 10 to 15 are written as A to F, so 11 becomes B. Writing 11 would look like two separate digits.
4. What is 200 in hexadecimal?
A. 8C
B. C8 ✓
200 ÷ 16 = 12 remainder 8, and 12 ÷ 16 = 0 remainder 12 (C). Reading the remainders from last to first gives C8.
5. What is 47 in hexadecimal?
A. 2F ✓
B. F2
47 ÷ 16 = 2 remainder 15 (F), and 2 ÷ 16 = 0 remainder 2. Reading from last to first gives 2F.

Match the Pairs

200 ÷ 16 = 12 remainder 8 → The first division step: the remainder 8 is the last hex digit (the right-hand digit) of the answer
12 → C → A remainder or quotient of 12 is written as the hex letter C
Read the remainders from last to first (bottom to top) to build the hex number → 200 ÷ 16 = 12 r 8, 12 ÷ 16 = 0 r 12, so 200 = C8
Check the answer by converting the hex back to denary → C8 = (12 × 16) + 8 = 200
200 = 8C → The remainders were read from first to last instead of last to first. The correct answer is C8.
promote 171 ÷ 16 = 10 r 11, so 171 = 1011 → The remainders 10 and 11 were written as the denary numbers 10 and 11 instead of the hex letters A and B. The correct answer is AB.

Key Term

divide by 16
Divide the denary number by 16 again and again. Read the remainders from last to first, writing 10 to 15 as A to F. Check by converting the hex back to denary.

Fill in the Blanks

1. 200 DIV 16 = 12 remainder 8
Hint: Type the number you divide by when converting denary to hexadecimal.
2. 200 MOD 16 = 8
Hint: Type the operator that gives the remainder after dividing.
3. Denary 12 is written as C in hex
Hint: Type the hex letter that stands for the denary value 12.
4. Remainders, first to last: 8, C Read last to first: C8
Hint: Type the hex number made by reading the remainders from last to first.
5. Check: C8 = 12 x 16 + 8 = 200
Hint: Type the denary value you get when converting the hex back.

Spot the Error

Question 1
A Convert 220 to hex
B 220 / 16 = 13 remainder 12
C 13 / 16 = 0 remainder 13
D Remainders first to last: CD
Line D — The remainders must be read from last to first, not first to last. The last remainder is 13 (D) and the first is 12 (C), so the answer is DC.
Question 2
A Convert 171 to hex
B 171 / 16 = 10 remainder 11
C 10 / 16 = 1 remainder 0
D Read bottom to top: AB
Line C — 10 is smaller than 16, so 10 / 16 = 0 remainder 10. The line should be 10 / 16 = 0 remainder 10, which gives the digit A.
Question 3
A Divide 47 by 8 each time
B 47 / 16 = 2 remainder 15
C 2 / 16 = 0 remainder 2
D Read last to first: 2F
Line A — Hexadecimal is base 16, so you divide by 16 each time. Dividing by 8 would give octal, not hex.
Question 4
A Convert 90 to hex
B 90 / 16 = 5 remainder 8
C 5 / 16 = 0 remainder 5
D 10 = A, so the answer is 5A
Line B — 5 x 16 = 80, and 90 - 80 = 10, so the remainder is 10, not 8. The line should be 90 / 16 = 5 remainder 10.
Question 5
A Convert 200 to hex
B 200 / 16 = 12 remainder 8
C 12 / 16 = 0 remainder 12
D 12 = B, so the answer is B8
Line D — In hex A = 10, B = 11 and C = 12. So 12 must be written as C, giving C8, not B8.

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