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10 questions · 20 marks
Computer systems manipulate bit patterns.
Convert the hexadecimal number D5 to denary.
Award one mark for:
213
Why: 13 × 16 + 5 = 213 (1).
93
Why: Takes the right-hand digit as the 16s, so the value is wrong.
18
Why: Adds the two digits instead of multiplying the first by 16.
Binary, denary and hexadecimal patterns represent numbers.
Convert the binary pattern 1100 1010 to hexadecimal.
Award one mark for each correct digit in the correct position:
Answer: CA
CA
Why: Each nibble is one hexadecimal digit: 1100 = C, 1010 = A: both digits are correct (2).
C10
Why: One digit is correct (1), but the second is written as 10 in denary instead of A.
AC
Why: The digits are the wrong way round, so neither is in the correct position.
Computer systems manipulate bit patterns.
Convert the binary pattern 1000 1010 to hexadecimal.
Award one mark for each correct digit in the correct position:
Answer: 8A
8A
Why: Each nibble is one hexadecimal digit: 1000 = 8, 1010 = A: both digits are correct (2).
810
Why: One digit is correct (1), but a digit over 9 is written in denary instead of as a letter.
A8
Why: The digits are the wrong way round, so neither is in the correct position.
Binary patterns can represent numbers.
Convert the binary pattern 1110 0100 to hexadecimal.
Award one mark for each correct digit in the correct position:
Answer: E4
E4
Why: Each nibble is one hexadecimal digit: 1110 = E, 0100 = 4: both digits are correct (2).
144
Why: One digit is correct (1), but a digit over 9 is written in denary instead of as a letter.
4E
Why: The digits are the wrong way round, so neither is in the correct position.
Computers manipulate binary patterns.
Convert the denary number 161 to hexadecimal.
Award one mark for each correct digit in the correct position:
Answer: A1
A1
Why: 161 ÷ 16 = 10 remainder 1, so the digits are A and 1: both digits are correct (2).
101
Why: One digit is correct (1), but a digit over 9 is written in denary instead of as a letter.
1A
Why: The digits are the wrong way round, so neither is in the correct position.
Computer systems manipulate bit patterns.
Convert the denary number -75 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.
1011 0101
Why: 75 is 01001011; flip the bits (10110100) and add 1: both nibbles are correct (2).
1011 0100
Why: Flips the bits of 75 but doesn't add 1. The first nibble is correct (1); the second is not.
1100 1011
Why: Uses sign and magnitude (a 1 in front of 75) instead of two's complement. Neither nibble is correct.
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 patterns can represent numbers.
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 | 1 | 0 |
| 0 | 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.
1111 0010
Why: 150 + 92 = 242, carrying where a column adds to 2: both nibbles are correct (2).
1111 0011
Why: A slip in the last bit. The first nibble is correct (1); the second is not.
1101 1110
Why: Writes 1 in every column with a 1 and never carries. Neither nibble is correct.
Computer systems manipulate bit patterns.
Complete the table to show the result of the 8-bit binary addition.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 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.
1101 0111
Why: 184 + 31 = 215, carrying where a column adds to 2: both nibbles are correct (2).
1010 0111
Why: Writes 0 for 1 + 1 but forgets to carry the 1. The second nibble is correct (1); the first is not.
1011 1111
Why: Writes 1 in every column with a 1 and never carries. 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 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
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.
0010 0100
Why: 193 + 99 = 292, which needs 9 bits; the 8 bits that are kept are both correct (2).
0010 0101
Why: A slip in the last bit. The first nibble is correct (1); the second is not.
1110 0011
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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