Converting denary to hexadecimal

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Quick Questions

Shade in the A or B circle for each question.

1. Which number do you repeatedly divide by to convert denary to hexadecimal?

A 16

B 2

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)

3. A remainder of 11 appears during a conversion. How do you write it in the hex answer?

A B

B 11

4. What is 200 in hexadecimal?

A 8C

B C8

5. What is 47 in hexadecimal?

A 2F

B F2

Match the Pairs

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

Left column		Right column
1200 ÷ 16 = 12 remainder 8		A200 ÷ 16 = 12 r 8, 12 ÷ 16 = 0 r 12, so 200 = C8
212 → C		BThe remainders were read from first to last instead of last to first. The correct answer is C8.
3Read the remainders from last to first (bottom to top) to build the hex number		CA remainder or quotient of 12 is written as the hex letter C
4Check the answer by converting the hex back to denary		DThe 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.
5200 = 8C		EThe first division step: the remainder 8 is the last hex digit (the right-hand digit) of the answer
6promote 171 ÷ 16 = 10 r 11, so 171 = 1011		FC8 = (12 × 16) + 8 = 200

Definitions

divide by 16

Fill in the Blanks

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

200 DIV __ = 12 remainder 8

200 ___ 16 = 8

Denary 12 is written as _ in hex

Remainders, first to last: 8, C Read last to first: __

Check: C8 = 12 x 16 + 8 = ___

Spot the Error

Shade in the letter of the line that contains an 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

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

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

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

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

Answer Key

Converting denary to hexadecimal

Section A: Quick Questions

A — 16

B — Last to first (bottom to top)

A — B

B — C8

A — 2F

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

200 DIV 16 = 12 remainder 8

200 MOD 16 = 8

Denary 12 is written as C in hex

Remainders, first to last: 8, C
Read last to first: C8

Check: C8 = 12 x 16 + 8 = 200

Section E: Spot the Error

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.

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.

A — Hexadecimal is base 16, so you divide by 16 each time. Dividing by 8 would give octal, not hex.

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.

D — In hex A = 10, B = 11 and C = 12. So 12 must be written as C, giving C8, not B8.