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5 questions · 9 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.
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.
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