Converting a denary number to 16-bit binary

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Converting a denary number to 16-bit binary

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. Which place value do you start with when converting a denary number to 16-bit binary?
A 65535
B 32768
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
3. Converting 1000: you write 1 under 512. What is the remainder to carry on with?
A 512
B 488
4. Which is denary 300 as 16-bit binary?
A 0000000100101100
B 100101100
5. Which is denary 5 as 16-bit binary?
A 0000000000000101
B 101
B

Match the Pairs

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

Left columnRight column
1300 - 256 = 44 AThe 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.
21000 < 2048 BLeading zeros are missing. This answer has only 9 digits, but a 16-bit answer needs 16 digits, so it should be 0000000100101100.
3Pad with leading zeros so the answer has 16 digits (shown here for 1000) C256 + 32 + 8 + 4 = 300
4Check your answer by adding the place values that have a 1 (shown here for 300) D0000 0011 1110 1000
5300 = 100101100 E256 fits in 300, so write 1 for the 256 place and carry on with the remainder 44
6Start at 1, then 2, 4, 8 ... and work up F2048 does not fit in 1000, so write 0 for the 2048 place and subtract nothing
C

Definitions

denary to 16-bit binary
D

Fill in the Blanks

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

1.
The first 16-bit place value is _____
2.
300 - ___ = 44, so write 1 for 256
3.
44 is less than 128, so write _ for 128
4.
10110 padded to 16 digits: ___________10110
5.
Check: 256 + 32 + 8 = ___
E

Spot the Error

Shade in the letter of the line that contains an 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
Question 2
A Place values start at 32768
B Then halve: 16384, 8192, 2048
C Continue down to 2, then 1
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
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
Question 5
A Convert 65535 to 16-bit binary
B Only 32768 fits
C Write sixteen 1s
D Answer: 1111111111111111

Answer Key

Converting a denary number to 16-bit binary
Section A: Quick Questions
Q1
B — 32768
Q2
A — 0, because 128 does not fit in 100
Q3
B — 488
Q4
A — 0000000100101100
Q5
A — 0000000000000101
Section B: Match the Pairs
Q1
300 - 256 = 44 → 256 fits in 300, so write 1 for the 256 place and carry on with the remainder 44
Q2
1000 < 2048 → 2048 does not fit in 1000, so write 0 for the 2048 place and subtract nothing
Q3
Pad with leading zeros so the answer has 16 digits (shown here for 1000) → 0000 0011 1110 1000
Q4
Check your answer by adding the place values that have a 1 (shown here for 300) → 256 + 32 + 8 + 4 = 300
Q5
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.
Q6
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.
Section C: Definitions
Q1
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.
Section D: Fill in the Blanks
Q1
The first 16-bit place value is 32768
Q2
300 - 256 = 44, so write 1 for 256
Q3
44 is less than 128, so write 0 for 128
Q4
10110 padded to 16 digits: 0000000000010110
Q5
Check: 256 + 32 + 8 = 296
Section E: Spot the Error
Q1
C — The subtraction is wrong. 44 - 32 = 12, not 22. A wrong remainder gives the wrong bits for the rest of the conversion.
Q2
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.
Q3
D — A 16-bit answer must keep its leading zeros so it has 16 digits. It should be 0000000000000101.
Q4
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.
Q5
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.