Paper 1 Data Representation Answers

These answers correspond to Paper 1 Data Representation Drills.

Answer 1: Binary to Denary

10101100
= 128 + 0 + 32 + 0 + 8 + 4 + 0 + 0
= 172

Mark points:

• uses correct 8-bit place values 128, 64, 32, 16, 8, 4, 2, 1;
• obtains denary 172.

Common weak answer:

• treating the binary digits as ordinary denary digits.

Answer 2: Denary to Binary

Using place values:

45 = 32 + 8 + 4 + 1

The 8-bit binary value is:

00101101

Mark points:

• decomposes 45 into powers of two;
• writes bits in correct 8-bit positions;
• includes leading zeroes to make 8 bits.

Common weak answer:

• giving 101101 without the requested 8-bit padding.

Answer 3: Hex to Binary

3 = 0011
A = 1010

So:

3A = 00111010

Mark points:

• maps 3 to 0011;
• maps A to 1010.

Common weak answer:

• converting A as if it were denary digit 1 or ignoring the letters A to F.

Answer 4: Binary to Hex

Group into nibbles:

11010110 = 1101 0110

Convert each nibble:

1101 = D
0110 = 6

So:

11010110 = D6

Mark points:

• groups the bits correctly into 1101 and 0110;
• converts the groups to D6.

Common weak answer:

• grouping from the left in uneven groups when the number of bits is not already a multiple of four. Pad on the left if needed.

Answer 5: Base Relationship

One hexadecimal digit represents exactly four binary bits. Therefore:

11111111 = 1111 1111 = FF

Hexadecimal is more compact because eight binary bits can be written as two hexadecimal digits without changing the underlying value.

Mark points:

• states one hex digit represents four bits;
• applies this to 11111111 = FF or explains compactness using the example.

Common weak answer:

• saying hexadecimal stores more information than binary. It is a shorter notation for the same bit pattern.

Answer 6: ASCII

ASCII stores characters as numeric codes. A and a have different codes because uppercase and lowercase letters are distinct characters, so each needs its own code value.

Mark points:

• ASCII maps characters to numeric codes;
• uppercase A and lowercase a are different characters with different codes.

Common weak answer:

• saying ASCII stores only numbers. ASCII uses numbers to represent characters.

Answer 7: Unicode

Unicode is needed because ASCII cannot represent all characters required by the page, such as Chinese characters 你 and 好, and symbols such as €. Unicode provides a much larger character set for many languages and symbols.

Mark points:

• identifies that ASCII is limited;
• links Unicode to representing many languages/symbols shown in the scenario.

Common weak answer:

• saying Unicode is only for making text bold or styled. Character encoding is about representing characters, not formatting.

Answer 8: Conversion Algorithm

Trace:

Current number	Remainder after division by 2	Next quotient
13	1	6
6	0	3
3	1	1
1	1	0

Read the remainders from bottom to top:

1101

Mark points:

• correct remainders 1, 0, 1, 1;
• correct quotients 6, 3, 1, 0;
• reads remainders in reverse order;
• gives binary 1101.

Common weak answer:

• reading the remainders from top to bottom as 1011, which is not 13.

Answer 9: Storage

Computer memory stores data using two-state patterns, represented as 0 and 1. Different data types are encoded into binary patterns using agreed formats, so image pixels, text characters, and sound samples can all be stored and processed as binary.

Mark points:

• hardware/memory uses two-state binary representation;
• different data types can be encoded using agreed binary formats.

Common weak answer:

• saying only numbers can be stored in binary. Text, images, and sound can also be encoded as binary patterns.

Answer 10: Error

The student added the bits as if each 1 had value 1. They ignored binary place values.

Correct working:

1011 = 8 + 0 + 2 + 1 = 11

Mark points:

• identifies that place values were ignored;
• uses correct place values 8, 4, 2, 1;
• gives denary 11.

Common weak answer:

• saying the answer is wrong because binary cannot be converted to denary. Binary values can be converted using place values.