Build a practice paper from 604 exam-style questions, each with its mark scheme and example answers. Print it, or answer it on paper and then open the mark schemes. Or browse the questions by topic.
10 questions · 19 marks
Binary, denary and hexadecimal patterns represent numbers.
Convert the binary pattern 1110 1100 to denary.
Award one mark for:
236
Why: Correct: 128 + 64 + 32 + 8 + 4 = 236 (1).
55
Why: Reads the place values from the wrong end (the left-hand bit as 1), so the value is wrong.
5
Why: Counts the 1s instead of adding their place values.
An electronic lock stores each of its codes as a 4-bit binary pattern.
Describe how the number of different codes that can be stored can be calculated.
Award up to two marks for a linked description such as:
Do not accept 15 (or 2^4 − 1): this is the largest value a 4-bit pattern can hold, not the number of different codes.
Do not award a response that only states 16 or '2^4 = 16' without a linked description.
Do not award '2 to the power of 4' on its own without a linked description, such as two values per bit or the number of bits used as the power of 2.
Each bit can be either 0 or 1, so there are two possibilities for every bit. For a 4-bit code this is 2 × 2 × 2 × 2 = 16 different codes.
Why: Two possible values for each bit (1) linked to multiplying for 4 bits to get 16 (1).
Each bit has two possible values.
Why: Gives the first point (1) but does not link it to calculating the number of codes.
The largest number a 4-bit pattern can hold is 15, so 15 different codes can be stored.
Why: Classic misconception: 15 is the largest value a 4-bit pattern can hold, not the number of different codes; the mark scheme says not to accept 15.
A computer stores a colour as a 24-bit binary pattern.
The programmer writes the colour in hexadecimal rather than in binary. Explain one reason why.
Award up to two marks for a linked explanation such as:
For both marks, the expansion must follow/associate with the statement.
Allow the 24-bit colour as the linked reason, e.g. a 24-bit value can be written as only 6 hexadecimal digits (1).
Do not accept 'easier'/'simpler' on its own: naming what is easier, such as easier to read/write, is the first mark, but the second mark needs a linked reason.
Only credit 'fewer digits/characters' once, as the reason for one point; do not award it again as the reason for a second point.
Do not accept that hexadecimal uses less storage space/memory than binary, or that it is more compact to store; the same number of bits is stored.
Hexadecimal is shorter than binary because each hexadecimal digit represents 4 bits, so the 24-bit colour needs only 6 hexadecimal digits.
Why: Gives the point that hexadecimal is shorter (1) and links it to each hexadecimal digit representing 4 bits, using the 24-bit colour as the linked reason (1).
Hexadecimal is easier to read than binary.
Why: Names what is easier to read (1) but gives no linked reason such as fewer digits to enter, so only one mark.
Hexadecimal is used because it takes up less storage space than binary.
Why: The same number of bits is stored in either notation, so this is a misconception and earns no mark.
Computers manipulate binary patterns.
Convert the binary pattern 1100 1111 to hexadecimal.
Award one mark for each correct digit in the correct position:
Answer: CF
CF
Why: Each nibble is one hexadecimal digit: 1100 = C, 1111 = F: both digits are correct (2).
C15
Why: One digit is correct (1), but the second is written as 15 in denary instead of F.
FC
Why: The digits are the wrong way round, so neither is in the correct position.
Computer systems manipulate bit patterns.
Convert the binary pattern 1110 1111 to hexadecimal.
Award one mark for each correct digit in the correct position:
Answer: EF
EF
Why: Each nibble is one hexadecimal digit: 1110 = E, 1111 = F: both digits are correct (2).
E15
Why: One digit is correct (1), but the second is written as 15 in denary instead of F.
FE
Why: The digits are the wrong way round, so neither is in the correct position.
Binary, denary and hexadecimal patterns represent numbers.
Convert the binary pattern 0100 1010 to hexadecimal.
Award one mark for each correct digit in the correct position:
Answer: 4A
4A
Why: Each nibble is one hexadecimal digit: 0100 = 4, 1010 = A: both digits are correct (2).
410
Why: One digit is correct (1), but a digit over 9 is written in denary instead of as a letter.
A4
Why: The digits are the wrong way round, so neither is in the correct position.
Computers manipulate binary patterns.
Convert the denary number 161 to hexadecimal.
Award one mark for each correct digit in the correct position:
Answer: A1
A1
Why: 161 ÷ 16 = 10 remainder 1, so the digits are A and 1: both digits are correct (2).
101
Why: One digit is correct (1), but a digit over 9 is written in denary instead of as a letter.
1A
Why: The digits are the wrong way round, so neither is in the correct position.
Binary patterns can represent numbers.
Convert the hexadecimal number D3 to 8-bit binary.
Award one mark for each correct nibble in the correct order:
0 marks if the response is not 8-bit binary.
1101 0011
Why: Each digit is 4 bits: D = 1101, 3 = 0011 (2).
1101 0100
Why: Converts 3 as if it were the next digit up. The first nibble is correct (1); the second is not.
0011 1101
Why: The nibbles are in the wrong order. Neither nibble is correct.
Binary, denary and hexadecimal patterns represent numbers.
Convert the hexadecimal number DB to 8-bit binary.
Award one mark for each correct nibble in the correct order:
0 marks if the response is not 8-bit binary.
1101 1011
Why: Each digit is 4 bits: D = 1101, B = 1011 (2).
1101 1100
Why: Converts B as if it were the next digit up. The first nibble is correct (1); the second is not.
1011 1101
Why: The nibbles are in the wrong order. Neither nibble is correct.
Computer systems manipulate bit patterns.
Complete the table with the result of applying the shift to the binary pattern.
| Binary pattern | Shift | 8-bit binary result |
|---|---|---|
| 1000 0111 | Logical shift right by 1 |
Award one mark for each correct nibble in the correct order:
0 marks if the response is not 8-bit binary.
0100 0011
Why: Every bit moves 1 place right, with 0s in from the left: both nibbles are correct (2).
0100 0010
Why: A slip in the last bit. The first nibble is correct (1); the second is not.
0000 1110
Why: Shifts the bits the wrong way. Neither nibble is correct.
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