Computers store all data as binary.
Convert the binary number 11110000 into hexadecimal.
Guidance
Correct answer only
Ignore case
F0
Why: 1111 is F and 0000 is 0: F0 (1).
150
Why: A digit over 9 is written in denary instead of as a letter (0).
F
Why: The final 0 is left off, which changes the value (0).
Computers store all data as binary.
Convert the hexadecimal number B4 into 8-bit binary.
Guidance
Correct answer only – binary must be 8 bits.
10110100
Why: B is 1011 and 4 is 0100 (1).
01001011
Why: The two nibbles are in the wrong order (0).
11 4
Why: Writes the denary value of each digit instead of its 4 bits (0).
Binary numbers can represent different forms of data.
Convert the hexadecimal number FE into denary.
Show your working.
2 marks for the correct answer
No marks for working on its own (e.g. multiplying by 16 (15 * 16 + 14), or converting to binary first (1111 1110)).
F = 15, E = 14
15 × 16 + 14 = 254
Why: The correct answer (2): the first digit times 16, plus the second.
1111 1100 = 252
Why: Converting to binary first is a correct method, but E is converted wrongly, so the answer is wrong (0).
15 + 14 = 29
Why: Adds the two digits instead of multiplying the first by 16, so neither mark (0).
Binary numbers can represent different forms of data.
Convert the hexadecimal number 6A into denary.
Show your working.
2 marks for the correct answer
No marks for working on its own (e.g. multiplying by 16 (6 * 16 + 10), or converting to binary first (0110 1010)).
6 = 6, A = 10
6 × 16 + 10 = 106
Why: The correct answer (2): the first digit times 16, plus the second.
0110 1000 = 104
Why: Converting to binary first is a correct method, but A is converted wrongly, so the answer is wrong (0).
6 + 10 = 16
Why: Adds the two digits instead of multiplying the first by 16, so neither mark (0).
Computers store all data as binary.
Convert the hexadecimal number B0 into denary.
Show your working.
2 marks for the correct answer
No marks for working on its own (e.g. multiplying by 16 (11 * 16 + 0), or converting to binary first (1011 0000)).
B = 11, 0 = 0
11 × 16 + 0 = 176
Why: The correct answer (2): the first digit times 16, plus the second.
1011 0001 = 177
Why: Converting to binary first is a correct method, but 0 is converted wrongly, so the answer is wrong (0).
11 + 0 = 11
Why: Adds the two digits instead of multiplying the first by 16, so neither mark (0).
Computers store all data as binary.
Add these two 8-bit binary numbers using binary addition.
Show your working out.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
2 marks for the correct binary answer
No marks for working on its own (the carries, or converting to denary and back).
Working, for example (no marks)
10111001
00101011
11100100
111 11
Carries: 111 11
Answer: 11100100
Why: The correct answer (2), with the 5 carries shown in the right columns.
Carries: 111 11
Answer: 01100100
Why: The five carries are right, but the left-hand bit of the answer is miswritten (0).
10111011
Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).
Binary numbers can represent different forms of data.
The following table has either the binary or denary value of 3 numbers.
Complete the table by converting each 8-bit binary number into denary and the denary number into 8-bit binary.
| 8-bit Binary | Denary |
|---|---|
| 00111101 | |
| 147 | |
| 10001000 |
1 mark each
8-bit Binary | Denary
00111101 | 61
10010011 | 147
10001000 | 136
Guidance
Binary must be 8 bits
61
10010011
136
Why: All three conversions are correct (3).
61
11001001
136
Why: The binary to denary conversions are right (2), but row 2 (binary) is back to front (0).
188
11001001
17
Why: None is right: row 1 (denary) reads the place values from the wrong end; row 2 (binary) is back to front; row 3 (denary) reads the place values from the wrong end (0).
Computers store all data as binary.
Complete the table by writing the missing denary, 8-bit binary or hexadecimal values.
| Denary | 8-bit binary | Hexadecimal |
|---|---|---|
| 41 | 29 | |
| 196 | C4 | |
| 10010101 | 95 | |
| 95 | 01011111 |
1 mark for each completed box
Denary | 8-bit binary | Hexadecimal
41 | 00101001 | 29
196 | 11000100 | C4
149 | 10010101 | 95
95 | 01011111 | 5F
Guidance
Correct answers only – binary must be 8 bits.
Ignore case in hex.
00101001
11000100
149
5F
Why: Every missing value is correct, and the binary is 8 bits (4).
101001
11000100
149
515
Why: Rows 2 and 3 are correct (2); row 1 (binary) leaves off the leading 0s, so it is not 8 bits (0) and row 4 (hexadecimal) has a digit over 9 written in denary (0).
101001
00100011
169
515
Why: None of the values is right: row 1 (binary) leaves off the leading 0s, so it is not 8 bits (0); row 2 (binary) is back to front (0); row 3 (denary) reads the place values from the wrong end (0); row 4 (hexadecimal) has a digit over 9 written in denary (0).
Binary numbers can represent different forms of data.
Each row in the table contains a number written as a denary value, an 8-bit binary value and a 2-digit hexadecimal value. Some values are missing.
Complete the table by writing in the missing value for each number.
| Denary | 8-bit binary | Hexadecimal |
|---|---|---|
| 01101100 | 6C | |
| 176 | B0 | |
| 173 | AD | |
| 123 | 01111011 |
1 mark for each completed box
Denary | 8-bit binary | Hexadecimal
108 | 01101100 | 6C
176 | 10110000 | B0
173 | 10101101 | AD
123 | 01111011 | 7B
Guidance
Correct answers only – binary must be 8 bits.
Ignore case in hex.
108
10110000
10101101
7B
Why: Every missing value is correct, and the binary is 8 bits (4).
54
10110000
10101101
711
Why: Rows 2 and 3 are correct (2); row 1 (denary) reads the place values from the wrong end (0) and row 4 (hexadecimal) has a digit over 9 written in denary (0).
54
00001101
10110101
711
Why: None of the values is right: row 1 (denary) reads the place values from the wrong end (0); row 2 (binary) is back to front (0); row 3 (binary) is back to front (0); row 4 (hexadecimal) has a digit over 9 written in denary (0).
Computers represent data in binary form.
Complete the table by writing the missing denary, 8-bit binary or hexadecimal values.
| Denary | 8-bit binary | Hexadecimal |
|---|---|---|
| 11100011 | E3 | |
| 168 | 10101000 | |
| 31 | 00011111 | |
| 196 | C4 |
1 mark for each completed box
Denary | 8-bit binary | Hexadecimal
227 | 11100011 | E3
168 | 10101000 | A8
31 | 00011111 | 1F
196 | 11000100 | C4
Guidance
Correct answers only – binary must be 8 bits.
Ignore case in hex.
227
A8
1F
11000100
Why: Every missing value is correct, and the binary is 8 bits (4).
199
A8
1F
00100011
Why: Rows 2 and 3 are correct (2); row 1 (denary) reads the place values from the wrong end (0) and row 4 (binary) is back to front (0).
199
108
115
00100011
Why: None of the values is right: row 1 (denary) reads the place values from the wrong end (0); row 2 (hexadecimal) has a digit over 9 written in denary (0); row 3 (hexadecimal) has a digit over 9 written in denary (0); row 4 (binary) is back to front (0).
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