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7 questions · 14 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.
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.
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.
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.
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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