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9 questions · 19 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 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 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.
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 patterns can represent numbers.
Complete the table to show the 8-bit result of the binary addition.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 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.
1011 0111
Why: 219 + 220 = 439, which needs 9 bits; the 8 bits that are kept are both correct (2).
0000 0111
Why: Forgets to carry the 1s. The second nibble is correct (1); the first is not.
1101 1111
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.
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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