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7 questions · 14 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.
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.
Computer systems manipulate bit patterns.
Convert the denary number -48 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 0000
Why: 48 is 00110000; flip the bits (11001111) and add 1: both nibbles are correct (2).
1011 0000
Why: Uses sign and magnitude (a 1 in front of 48) instead of two's complement. The second nibble is correct (1); the first is not.
1100 1111
Why: Flips the bits of 48 but doesn't add 1. Neither nibble is correct.
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, 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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