← IGCSE Computer Science Paper 1

Converting a denary number to 16-bit binary

Work from 32768 down to 1. Write 1 and subtract if the place value fits in the remainder, otherwise write 0. Keep leading zeros so the answer has 16 digits.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 12

Understanding Converting a denary number to 16-bit binary in IGCSE Computer Science Paper 1

What it does: The places 32768 down to 1024 are all 0 for 1000. They must still be written so the answer is 16 digits long. Adding the place values under each 1 should give the original denary number. If it does, the conversion is correct. Write 1 only if the place value fits into the remainder. 128 is bigger than 100, so write 0 and subtract nothing. 5 = 4 + 1, but a 16-bit answer needs 16 digits. Keep the leading zeros.

Common mistakes: The subtraction is wrong. 44 - 32 = 12, not 22. A wrong remainder gives the wrong bits for the rest of the conversion. Each 16-bit place value is half the one before it. Half of 8192 is 4096, not 2048, so the sequence is 16384, 8192, 4096.

Class: _____________________  ·  Name: _____________________  ·  Date: _________

Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

🖨 Print worksheet + answer key Add Converting a denary number to 16-bit binary to a class →

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

Take this worksheet further — free with Cloodit

Each concept is reinforced from every angle — learned, then applied, then tested.

Learning
Duo
Which place value do you start with when converting a denary number to 16-bit binary?
6553532768
Matches
300 = 100101100
↓
Leading zeros are missing. This answer has only 9 digits, but a 16-bit answer needs 16 digits, so it should be 0000000100101100.
Applying
Meanings
Term
denary to 16-bit binary
Meaning
Work from 32768 down to 1. Write 1 and subtract if the place value fits in the remainder, otherwise write 0. Keep leading zeros so the answer has 16 digits.
Practice
1000 = 512 + 256 + 128 + 64 + 32 + 8
Testing
Gaps
The first 16-bit place value is
Check Answer
Spots
2256 fits: 300 - 256 = 44
332 fits: 44 - 32 = 22

Cloodit turns curriculum-aligned coding content into journeys students work through one biome at a time.

The 'Platinum Fox' badge — Tundra Legend, one of Cloodit's 106 collectible badges
Students earn collectable badges

Over 100 of them, across seven natural biomes.

Study Buddy
Students build a real study resource

Turns their work into revision material ready for Flash Cards and Exam study.

Diamond Dash — one of Cloodit's live, competitive Sprint games
Students lock in with Sprints

Live, competitive practice for the start of the lesson or a teacher-led lesson finisher.

A Cloodit certificate of achievement, ready to personalise and print
Custom printable certificates

Honour your top performers, or encourage a student who's trying hard — ready to print in seconds.

Add to class →

Quick Questions

1. Which place value do you start with when converting a denary number to 16-bit binary?
A. 65535
B. 32768 ✓
The 16 place values run from 32768 down to 1. 65535 is the largest number 16 bits can store, not a place value.
2. You are converting a number and the remainder is 100. What do you write for the 128 place?
A. 0, because 128 does not fit in 100 ✓
B. 1, because 128 is close to 100
Write 1 only if the place value fits into the remainder. 128 is bigger than 100, so write 0 and subtract nothing.
3. Converting 1000: you write 1 under 512. What is the remainder to carry on with?
A. 512
B. 488 ✓
Subtract the place value that fitted: 1000 - 512 = 488. Then carry on with 256 and the rest of the place values.
4. Which is denary 300 as 16-bit binary?
A. 0000000100101100 ✓
B. 100101100
300 = 256 + 32 + 8 + 4. You must pad with leading zeros so the answer has all 16 digits.
5. Which is denary 5 as 16-bit binary?
A. 0000000000000101 ✓
B. 101
5 = 4 + 1, but a 16-bit answer needs 16 digits. Keep the leading zeros.

Match the Pairs

300 - 256 = 44 → 256 fits in 300, so write 1 for the 256 place and carry on with the remainder 44
1000 < 2048 → 2048 does not fit in 1000, so write 0 for the 2048 place and subtract nothing
Pad with leading zeros so the answer has 16 digits (shown here for 1000) → 0000 0011 1110 1000
Check your answer by adding the place values that have a 1 (shown here for 300) → 256 + 32 + 8 + 4 = 300
300 = 100101100 → Leading zeros are missing. This answer has only 9 digits, but a 16-bit answer needs 16 digits, so it should be 0000000100101100.
Start at 1, then 2, 4, 8 ... and work up → The method starts at the wrong end. You must start at 32768 and work down to 1, checking whether each place value fits in the remainder.

Key Term

denary to 16-bit binary
Work from 32768 down to 1. Write 1 and subtract if the place value fits in the remainder, otherwise write 0. Keep leading zeros so the answer has 16 digits.

Fill in the Blanks

1. The first 16-bit place value is 32768
Hint: Type the place value of the leftmost bit in a 16-bit number, where you start the conversion.
2. 300 - 256 = 44, so write 1 for 256
Hint: Type the first place value that fits into 300, the one that gets subtracted and leaves 44.
3. 44 is less than 128, so write 0 for 128
Hint: Type the bit you write when the place value does not fit in the remainder.
4. 10110 padded to 16 digits: 0000000000010110
Hint: Type the leading zeros needed to make the number up to 16 digits.
5. Check: 256 + 32 + 8 = 296
Hint: Type the total of the place values that have a 1, which should match the original denary number.

Spot the Error

Question 1
A Convert 300 to 16-bit binary
B 256 fits: 300 - 256 = 44
C 32 fits: 44 - 32 = 22
D Answer: 0000000100101100
Line C — The subtraction is wrong. 44 - 32 = 12, not 22. A wrong remainder gives the wrong bits for the rest of the conversion.
Question 2
A Place values start at 32768
B Then halve: 16384, 8192, 2048
C Continue down to 2, then 1
Line B — Each 16-bit place value is half the one before it. Half of 8192 is 4096, not 2048, so the sequence is 16384, 8192, 4096.
Question 3
A Convert 5 to 16-bit binary
B 4 fits: 5 - 4 = 1
C 1 fits: 1 - 1 = 0
D Answer: 101
E Check: 4 + 1 = 5
Line D — A 16-bit answer must keep its leading zeros so it has 16 digits. It should be 0000000000000101.
Question 4
A Convert 40 to 16-bit binary
B 32 fits: 40 - 32 = 8
C 16 does not fit, write 0
D 8 does not fit, write 0
E Answer: 0000000000101000
Line D — The remainder is 8 and the place value is 8, so it fits. Write 1 and subtract to leave 0. The answer 0000000000101000 has a 1 in the 8 place.
Question 5
A Convert 65535 to 16-bit binary
B Only 32768 fits
C Write sixteen 1s
D Answer: 1111111111111111
Line B — 65535 is the largest 16-bit number, so every place value from 32768 to 1 fits. That gives sixteen 1s, not just a single 1.

Student with a class code? Join your class →