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9 questions · 17 marks
Computers manipulate binary patterns.
Convert the binary pattern 1010 0100 to denary.
Award one mark for:
164
Why: Correct: 128 + 32 + 4 = 164 (1).
37
Why: Reads the place values from the wrong end (the left-hand bit as 1), so the value is wrong.
3
Why: Counts the 1s instead of adding their place values.
Computers represent all data using binary.
Explain one reason why computers use binary to represent data.
Award up to two marks for a linked explanation such as:
For both marks, the expansion must follow/associate with the statement.
Do not accept 'computers only understand 0s and 1s' as a reason on its own without saying what the two states are or why binary matches them.
Do not accept 'computers are digital' or 'that is how computers work' without expansion.
Do not accept 'binary is easier to read/write' or 'binary is easier to understand' as a reason for using binary.
Do not award the same point twice if it is repeated in different words, e.g. two answers that both say circuits/components are on or off.
Computers use binary because their electronic circuits have two states, on and off. Binary also has only two values, 0 and 1, so these can represent the states of the circuit.
Why: Links the two circuit states (1) to binary's two values representing them (1).
Computers use binary because their circuits are either on or off.
Why: Identifies the two circuit states (1) but does not link them to binary's two values, so the second mark is not awarded.
Computers use binary because it is easier to read than denary.
Why: 'Easier to read' is a reason for using hexadecimal, not a correct reason for using binary; the mark scheme tells markers not to accept it, so no mark.
Computers manipulate binary patterns.
Convert the denary number 184 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.
1011 1000
Why: 184 = 128 + 32 + 16 + 8: both nibbles are correct (2).
1011 1001
Why: Converts 185 instead (a slip in adding up the place values). The first nibble is correct (1); the second is not.
0001 1101
Why: The bits are written in reverse, smallest place value first. Neither nibble is correct.
Computer systems manipulate bit patterns.
Convert the hexadecimal number D5 to denary.
Award one mark for:
213
Why: 13 × 16 + 5 = 213 (1).
93
Why: Takes the right-hand digit as the 16s, so the value is wrong.
18
Why: Adds the two digits instead of multiplying the first by 16.
Binary patterns can represent numbers.
Convert the 8-bit binary two's complement pattern 1111 1001 to denary.
Award one mark for each of:
The correct answer is −7
−7
Why: The left-hand bit is worth −128: −128 + 121 = -7. Sign (1) and value (1).
7
Why: The value is right (1) but the minus sign is missing.
249
Why: Reads it as an unsigned number, so neither the sign nor the value is right.
Binary, denary and hexadecimal patterns represent numbers.
Convert the denary number -46 to 8-bit binary using two's complement.
Award one mark for each correct nibble in the correct order:
0 marks if the response is not 8-bit binary.
1101 0010
Why: 46 is 00101110; flip the bits (11010001) and add 1: both nibbles are correct (2).
1101 0001
Why: Flips the bits of 46 but doesn't add 1. The first nibble is correct (1); the second is not.
1010 1110
Why: Uses sign and magnitude (a 1 in front of 46) instead of two's complement. Neither nibble is correct.
Computer systems manipulate bit patterns.
Convert the 8-bit binary two's complement pattern 1100 1011 to denary.
Award one mark for each of:
The correct answer is −53
−53
Why: The left-hand bit is worth −128: −128 + 75 = -53. Sign (1) and value (1).
53
Why: The value is right (1) but the minus sign is missing.
203
Why: Reads it as an unsigned number, so neither the sign nor the value is right.
Binary, denary and hexadecimal patterns represent numbers.
Complete the table with the result of applying the shift to the binary pattern.
| Binary pattern | Shift | 8-bit binary result |
|---|---|---|
| 1010 1100 | Arithmetic 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.
1101 0110
Why: Every bit moves 1 place right, with copies of the sign bit (1) in from the left: both nibbles are correct (2).
0101 0110
Why: Fills the gap on the left with 0s, as a logical shift would, instead of copying the sign bit. The second nibble is correct (1); the first is not.
0101 1000
Why: Shifts the bits the wrong way. Neither nibble is correct.
Computers manipulate binary patterns.
Complete the table to show the 8-bit result of the binary addition.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
Award one mark for each correct nibble in the correct order:
0 marks if the response is not 8-bit binary.
Ignore a carry shown beyond the eighth bit.
0111 0101
Why: 185 + 188 = 373, which needs 9 bits; the 8 bits that are kept are both correct (2).
0000 0101
Why: Forgets to carry the 1s. The second nibble is correct (1); the first is not.
1011 1101
Why: Never carries. Neither nibble is correct.
State the name of the error that occurs when this addition is carried out.
Award one mark for:
Overflow
Why: The result needs more bits than are available (1).
Underflow
Why: A near miss: the result is too big for 8 bits, not too small.
A syntax error
Why: A syntax error is a mistake in a program's code, not in arithmetic.
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