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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.
A traffic light controller uses a 5-bit binary pattern to store the state of its lights.
Explain why this pattern can represent a maximum of 32 different states.
Award up to two marks for a linked explanation such as:
For both marks, the expansion must follow/associate with the statement.
Do not award a response that only repeats the 32 states given in the question, such as 'it can represent 32 states' or '2^5 = 32', without a reason about each bit having two possible values.
Do not accept 2 × 5 = 10 as the calculation; the number of states doubles with each extra bit.
Do not accept 31/0 to 31 as the number of states; 31 is the largest value five bits can store, not the number of states.
There are 32 different states because each of the 5 bits has two possible values, 0 and 1, so the number of combinations is 2 × 2 × 2 × 2 × 2 = 32.
Why: Point that each bit has two possible values, 0 and 1 (1), linked to the calculation 2 × 2 × 2 × 2 × 2 = 32 states (1).
Each bit has two possible values, 0 and 1.
Why: Gives the point that each bit has two possible values (1) but does not link it to 2^5 = 32, so the second mark is not earned.
It can represent 32 states because the highest number it can store is 31.
Why: Only repeats the 32 states from the question and gives the common misconception that 31 is the number of states; there is no reason about each bit having two possible values, so no marks.
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 denary number 140 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.
1000 1100
Why: 140 = 128 + 8 + 4: both nibbles are correct (2).
1000 1101
Why: Converts 141 instead (a slip in adding up the place values). The first nibble is correct (1); the second is not.
0011 0001
Why: The bits are written in reverse, smallest place value first. Neither nibble is correct.
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.
Computer systems manipulate bit patterns.
Convert the 8-bit binary two's complement pattern 1000 0111 to denary.
Award one mark for each of:
The correct answer is −121
−121
Why: The left-hand bit is worth −128: −128 + 7 = -121. Sign (1) and value (1).
121
Why: The value is right (1) but the minus sign is missing.
135
Why: Reads it as an unsigned number, so neither the sign nor the value is right.
Computers manipulate binary patterns.
Complete the table to show the result of the 8-bit binary addition.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
Award one mark for each correct nibble in the correct order:
0 marks if the response is not 8-bit binary.
1110 0100
Why: 149 + 79 = 228, carrying where a column adds to 2: both nibbles are correct (2).
1110 0101
Why: A slip in the last bit. The first nibble is correct (1); the second is not.
1101 1111
Why: Writes 1 in every column with a 1 and never carries. 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 |
|---|---|---|
| 0011 0100 | Logical shift left by 3 |
Award one mark for each correct nibble in the correct order:
0 marks if the response is not 8-bit binary.
1010 0000
Why: Every bit moves 3 places left, with 0s in from the right: both nibbles are correct (2).
1101 0000
Why: Shifts 2 places instead of 3. The second nibble is correct (1); the first is not.
0000 0110
Why: Shifts the bits the wrong way. 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 |
|---|---|---|
| 1100 0001 | Arithmetic shift right by 2 |
Award one mark for each correct nibble in the correct order:
0 marks if the response is not 8-bit binary.
1111 0000
Why: Every bit moves 2 places right, with copies of the sign bit (1) in from the left: both nibbles are correct (2).
0011 0000
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.
0000 0100
Why: Shifts the bits the wrong way. Neither nibble is correct.
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