Adding Binary Numbers exam questions

12 OCR GCSE Computer Science (J277) exam-style questions on Adding Binary Numbers (1.2 Memory & Storage), 24 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	30 minutes

1Binary addition, shifts and number facts2 marks

Computers store all data as binary.

Complete the binary addition of these two 8-bit binary numbers.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
0	0	1	1	0	1	1	0
0	0	0	1	1	0	1	1

Mark scheme

2 marks for the correct binary answer

01010001

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

00110110

00011011

01010001

11111

Example answers and how they were marked

Full marks2/2

Carries: 11111

Answer: 01010001

Why: The correct answer (2), with the 5 carries shown in the right columns.

No marks0/2

Carries: 11111

Answer: 11010001

Why: The five carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

00111111

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

2Binary addition, shifts and number facts2 marks

Computers represent data in binary form.

Add these two 8-bit binary numbers using binary addition.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
0	0	0	1	1	1	1	0
1	0	0	1	1	1	1	0

Mark scheme

2 marks for the correct binary answer

10111100

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

00011110

10011110

10111100

1111

Example answers and how they were marked

Full marks2/2

Carries: 1111

Answer: 10111100

Why: The correct answer (2), with the 4 carries shown in the right columns.

No marks0/2

Carries: 1111

Answer: 00111100

Why: The four carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

10011110

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

3Binary addition, shifts and number facts2 marks

Binary numbers can represent different forms of data.

Complete the binary addition of these two 8-bit binary numbers.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
0	0	0	1	0	1	1	1
0	0	0	1	0	1	1	1

Mark scheme

2 marks for the correct binary answer

00101110

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

00010111

00101110

1 111

Example answers and how they were marked

Full marks2/2

Carries: 1 111

Answer: 00101110

Why: The correct answer (2), with the 4 carries shown in the right columns.

No marks0/2

Carries: 1 111

Answer: 10101110

Why: The four carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

00010111

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

4Binary addition, shifts and number facts2 marks

Computers represent data in binary form.

Add these two 8-bit binary numbers using binary addition.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
0	1	1	1	0	0	0	0
0	1	1	0	1	0	0	1

Mark scheme

2 marks for the correct binary answer

11011001

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

01110000

01101001

11011001

Example answers and how they were marked

Full marks2/2

Carries: 11

Answer: 11011001

Why: The correct answer (2), with the 2 carries shown in the right columns.

No marks0/2

Carries: 11

Answer: 01011001

Why: The two carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

01111001

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

5Binary addition, shifts and number facts2 marks

Computers represent data in binary form.

Add these two 8-bit binary numbers using binary addition.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
0	1	0	0	1	0	1	0
0	1	1	1	1	0	1	0

Mark scheme

2 marks for the correct binary answer

11000100

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

01001010

01111010

11000100

1111 1

Example answers and how they were marked

Full marks2/2

Carries: 1111 1

Answer: 11000100

Why: The correct answer (2), with the 5 carries shown in the right columns.

No marks0/2

Carries: 1111 1

Answer: 01000100

Why: The five carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

01111010

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

6Binary addition, shifts and number facts2 marks

Binary numbers can represent different forms of data.

Add these two 8-bit binary numbers using binary addition.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
1	0	0	1	0	1	1	1
0	1	0	0	1	1	0	0

Mark scheme

2 marks for the correct binary answer

11100011

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

10010111

01001100

11100011

111

Example answers and how they were marked

Full marks2/2

Carries: 111

Answer: 11100011

Why: The correct answer (2), with the 3 carries shown in the right columns.

No marks0/2

Carries: 111

Answer: 01100011

Why: The three carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

11011111

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

7Binary addition, shifts and number facts2 marks

Computers represent data in binary form.

Add these two 8-bit binary numbers using binary addition.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
0	1	1	1	0	1	1	0
0	1	1	0	0	1	1	1

Mark scheme

2 marks for the correct binary answer

11011101

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

01110110

01100111

11011101

11 11

Example answers and how they were marked

Full marks2/2

Carries: 11 11

Answer: 11011101

Why: The correct answer (2), with the 4 carries shown in the right columns.

No marks0/2

Carries: 11 11

Answer: 01011101

Why: The four carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

01110111

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

8Binary addition, shifts and number facts2 marks

Computers store all data as binary.

Complete the binary addition of these two 8-bit binary numbers.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
1	0	0	0	1	0	0	0
0	0	0	1	1	1	1	1

Mark scheme

2 marks for the correct binary answer

10100111

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

10001000

00011111

10100111

Example answers and how they were marked

Full marks2/2

Carries: 11

Answer: 10100111

Why: The correct answer (2), with the 2 carries shown in the right columns.

No marks0/2

Carries: 11

Answer: 00100111

Why: The two carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

10011111

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

9Binary addition, shifts and number facts2 marks

Computers represent data in binary form.

Add these two 8-bit binary numbers using binary addition.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
1	0	1	0	1	0	1	0
0	0	0	1	1	0	1	0

Mark scheme

2 marks for the correct binary answer

11000100

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

10101010

00011010

11000100

111 1

Example answers and how they were marked

Full marks2/2

Carries: 111 1

Answer: 11000100

Why: The correct answer (2), with the 4 carries shown in the right columns.

No marks0/2

Carries: 111 1

Answer: 01000100

Why: The four carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

10111010

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

10Binary addition, shifts and number facts2 marks

Binary numbers can represent different forms of data.

Complete the binary addition of these two 8-bit binary numbers.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
0	0	1	1	0	1	0	0
0	1	0	1	0	0	1	1

Mark scheme

2 marks for the correct binary answer

10000111

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

00110100

01010011

10000111

111

Example answers and how they were marked

Full marks2/2

Carries: 111

Answer: 10000111

Why: The correct answer (2), with the 3 carries shown in the right columns.

No marks0/2

Carries: 111

Answer: 00000111

Why: The three carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

01110111

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

11Binary addition, shifts and number facts2 marks

Binary numbers can represent different forms of data.

Complete the binary addition of these two 8-bit binary numbers.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
0	1	1	0	1	1	0	1
0	1	0	1	1	1	0	0

Mark scheme

2 marks for the correct binary answer

11001001

No marks for working on its own (the carries, or converting to denary and back).

Working, for example (no marks)

01101101

01011100

11001001

11111

Example answers and how they were marked

Full marks2/2

Carries: 11111

Answer: 11001001

Why: The correct answer (2), with the 5 carries shown in the right columns.

No marks0/2

Carries: 11111

Answer: 01001001

Why: The five carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

01111101

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

12Binary addition, shifts and number facts2 marks

Computers store all data as binary.

Add these two 8-bit binary numbers using binary addition.

Show your working out.

[2 marks]

128	64	32	16	8	4	2	1
1	0	1	1	1	0	0	1
0	0	1	0	1	0	1	1

Mark scheme

2 marks for the correct binary answer

11100100

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

Example answers and how they were marked

Full marks2/2

Carries: 111 11

Answer: 11100100

Why: The correct answer (2), with the 5 carries shown in the right columns.

No marks0/2

Carries: 111 11

Answer: 01100100

Why: The five carries are right, but the left-hand bit of the answer is miswritten (0).

No marks0/2

10111011

Why: A 1 is written in every column with a 1 and nothing is carried, so neither mark (0).

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