Denary to Binary Conversion exam questions

12 OCR GCSE Computer Science (J277) exam-style questions on Denary to Binary Conversion (1.2 Memory & Storage), 30 marks in all. Answer them on paper or print them, then open the mark schemes and example answers to see how each is marked.

Name
Class
Suggested time	40 minutes

1Convert2 marks

Computers store all data as binary.

Convert the denary number 104 into 8-bit binary.

Show your working.

[2 marks]

Mark scheme

2 marks for the correct answer

01101000

No marks for working on its own (e.g. dividing by 2, or writing the place values (128, 64, 32, 16, 8, 4, 2, 1) with the binary below and subtracting).

Guidance

Binary must be 8 bits.

Example answers and how they were marked

Full marks2/2

128 64 32 16 8 4 2 1

0 1 1 0 1 0 0 0

104 − 64 = 40, 40 − 32 = 8, 8 − 8 = 0

Answer: 01101000

Why: The correct 8-bit answer (2); the place values and subtractions show how it was found.

No marks0/2

1 2 4 8 16 32 64 128

0 0 0 1 0 1 1 0

Answer: 00010110

Why: The place values are written smallest first, so the answer comes out back to front and is wrong (0).

No marks0/2

01100000

Why: No working (0), and the 1 bit is missed, so the answer is wrong (0).

2Convert2 marks

Computers store all data as binary.

Convert the denary number 252 into 8-bit binary.

Show your working.

[2 marks]

Mark scheme

2 marks for the correct answer

11111100

No marks for working on its own (e.g. dividing by 2, or writing the place values (128, 64, 32, 16, 8, 4, 2, 1) with the binary below and subtracting).

Guidance

Binary must be 8 bits.

Example answers and how they were marked

Full marks2/2

128 64 32 16 8 4 2 1

1 1 1 1 1 1 0 0

252 − 128 = 124, 124 − 64 = 60, 60 − 32 = 28, 28 − 16 = 12, 12 − 8 = 4, 4 − 4 = 0

Answer: 11111100

Why: The correct 8-bit answer (2); the place values and subtractions show how it was found.

No marks0/2

1 2 4 8 16 32 64 128

0 0 1 1 1 1 1 1

Answer: 00111111

Why: The place values are written smallest first, so the answer comes out back to front and is wrong (0).

No marks0/2

11111000

Why: No working (0), and the 1 bit is missed, so the answer is wrong (0).

3Convert2 marks

Computers store all data as binary.

Convert the denary number 89 into 8-bit binary.

Show your working.

[2 marks]

Mark scheme

2 marks for the correct answer

01011001

No marks for working on its own (e.g. dividing by 2, or writing the place values (128, 64, 32, 16, 8, 4, 2, 1) with the binary below and subtracting).

Guidance

Binary must be 8 bits.

Example answers and how they were marked

Full marks2/2

128 64 32 16 8 4 2 1

0 1 0 1 1 0 0 1

89 − 64 = 25, 25 − 16 = 9, 9 − 8 = 1, 1 − 1 = 0

Answer: 01011001

Why: The correct 8-bit answer (2); the place values and subtractions show how it was found.

No marks0/2

1 2 4 8 16 32 64 128

1 0 0 1 1 0 1 0

Answer: 10011010

Why: The place values are written smallest first, so the answer comes out back to front and is wrong (0).

No marks0/2

01011000

Why: No working (0), and the 1 bit is missed, so the answer is wrong (0).

4Convert2 marks

Computers represent data in binary form.

Convert the denary number 111 into 8-bit binary.

Show your working.

[2 marks]

Mark scheme

2 marks for the correct answer

01101111

No marks for working on its own (e.g. dividing by 2, or writing the place values (128, 64, 32, 16, 8, 4, 2, 1) with the binary below and subtracting).

Guidance

Binary must be 8 bits.

Example answers and how they were marked

Full marks2/2

128 64 32 16 8 4 2 1

0 1 1 0 1 1 1 1

111 − 64 = 47, 47 − 32 = 15, 15 − 8 = 7, 7 − 4 = 3, 3 − 2 = 1, 1 − 1 = 0

Answer: 01101111

Why: The correct 8-bit answer (2); the place values and subtractions show how it was found.

No marks0/2

1 2 4 8 16 32 64 128

1 1 1 1 0 1 1 0

Answer: 11110110

Why: The place values are written smallest first, so the answer comes out back to front and is wrong (0).

No marks0/2

01101110

Why: No working (0), and the 1 bit is missed, so the answer is wrong (0).

5Convert2 marks

Binary numbers can represent different forms of data.

Convert the denary number 103 into 8-bit binary.

Show your working.

[2 marks]

Mark scheme

2 marks for the correct answer

01100111

No marks for working on its own (e.g. dividing by 2, or writing the place values (128, 64, 32, 16, 8, 4, 2, 1) with the binary below and subtracting).

Guidance

Binary must be 8 bits.

Example answers and how they were marked

Full marks2/2

128 64 32 16 8 4 2 1

0 1 1 0 0 1 1 1

103 − 64 = 39, 39 − 32 = 7, 7 − 4 = 3, 3 − 2 = 1, 1 − 1 = 0

Answer: 01100111

Why: The correct 8-bit answer (2); the place values and subtractions show how it was found.

No marks0/2

1 2 4 8 16 32 64 128

1 1 1 0 0 1 1 0

Answer: 11100110

Why: The place values are written smallest first, so the answer comes out back to front and is wrong (0).

No marks0/2

01100110

Why: No working (0), and the 1 bit is missed, so the answer is wrong (0).

6Convert2 marks

Binary numbers can represent different forms of data.

Convert the denary number 126 into 8-bit binary.

Show your working.

[2 marks]

Mark scheme

2 marks for the correct answer

01111110

No marks for working on its own (e.g. dividing by 2, or writing the place values (128, 64, 32, 16, 8, 4, 2, 1) with the binary below and subtracting).

Guidance

Binary must be 8 bits.

Example answers and how they were marked

Full marks2/2

128 64 32 16 8 4 2 1

0 1 1 1 1 1 1 0

126 − 64 = 62, 62 − 32 = 30, 30 − 16 = 14, 14 − 8 = 6, 6 − 4 = 2, 2 − 2 = 0

Answer: 01111110

Why: The correct 8-bit answer (2); the place values and subtractions show how it was found.

No marks0/2

1 2 4 8 16 32 64 128

0 1 1 1 1 1 1 0

Answer: 01111111

Why: The place values are written smallest first and the last bit is miscopied, so the answer is wrong (0).

No marks0/2

01111100

Why: No working (0), and the 1 bit is missed, so the answer is wrong (0).

7Convert3 marks

Computers store all data as binary.

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.

[3 marks]

8-bit Binary	Denary
01100010
10110101
	59

Mark scheme

1 mark each

8-bit Binary | Denary

01100010 | 98

10110101 | 181

00111011 | 59

Guidance

Binary must be 8 bits

Example answers and how they were marked

Full marks3/3

181

00111011

Why: All three conversions are correct (3).

Some marks2/3

181

111011

Why: The binary to denary conversions are right (2), but row 3 (binary) leaves off the leading 0s, so it is not 8 bits (0).

No marks0/3

173

111011

Why: None is right: row 1 (denary) reads the place values from the wrong end; row 2 (denary) reads the place values from the wrong end; row 3 (binary) leaves off the leading 0s, so it is not 8 bits (0).

8Convert3 marks

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.

[3 marks]

8-bit Binary	Denary
11011011
11100100
	182

Mark scheme

1 mark each

8-bit Binary | Denary

11011011 | 219

11100100 | 228

10110110 | 182

Guidance

Binary must be 8 bits

Example answers and how they were marked

Full marks3/3

219

228

10110110

Why: All three conversions are correct (3).

Some marks2/3

219

228

01101101

Why: The binary to denary conversions are right (2), but row 3 (binary) is back to front (0).

No marks0/3

220

01101101

Why: None is right: row 1 (denary) is a slip in adding the place values; row 2 (denary) reads the place values from the wrong end; row 3 (binary) is back to front (0).

9Convert3 marks

Computers represent data in binary form.

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.

[3 marks]

8-bit Binary	Denary
11001100
	155
11111000

Mark scheme

1 mark each

8-bit Binary | Denary

11001100 | 204

10011011 | 155

11111000 | 248

Guidance

Binary must be 8 bits

Example answers and how they were marked

Full marks3/3

204

10011011

248

Why: All three conversions are correct (3).

Some marks2/3

204

11011001

248

Why: The binary to denary conversions are right (2), but row 2 (binary) is back to front (0).

No marks0/3

11011001

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).

10Convert3 marks

Computers store all data as binary.

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.

[3 marks]

8-bit Binary	Denary
01110111
	135
00100010

Mark scheme

1 mark each

8-bit Binary | Denary

01110111 | 119

10000111 | 135

00100010 | 34

Guidance

Binary must be 8 bits

Example answers and how they were marked

Full marks3/3

119

10000111

Why: All three conversions are correct (3).

Some marks2/3

119

11100001

Why: The binary to denary conversions are right (2), but row 2 (binary) is back to front (0).

No marks0/3

238

11100001

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).

11Convert3 marks

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.

[3 marks]

8-bit Binary	Denary
11110110
	233
01101000

Mark scheme

1 mark each

8-bit Binary | Denary

11110110 | 246

11101001 | 233

01101000 | 104

Guidance

Binary must be 8 bits

Example answers and how they were marked

Full marks3/3

246

11101001

104

Why: All three conversions are correct (3).

Some marks2/3

246

10010111

104

Why: The binary to denary conversions are right (2), but row 2 (binary) is back to front (0).

No marks0/3

111

10010111

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).

12Convert3 marks

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.

[3 marks]

8-bit Binary	Denary
10000001
10011101
	159

Mark scheme

1 mark each

8-bit Binary | Denary

10000001 | 129

10011101 | 157

10011111 | 159

Guidance

Binary must be 8 bits

Example answers and how they were marked

Full marks3/3

129

157

10011111

Why: All three conversions are correct (3).

Some marks2/3

129

157

11111001

Why: The binary to denary conversions are right (2), but row 3 (binary) is back to front (0).

No marks0/3

130

185

11111001

Why: None is right: row 1 (denary) is a slip in adding the place values; row 2 (denary) reads the place values from the wrong end; row 3 (binary) is back to front (0).

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