Adding Binary Numbers exam questions

6 Edexcel GCSE Computer Science (1CP2) exam-style questions on Adding Binary Numbers (2.1 Binary), 15 marks in all. Answer them on paper or print them, then open the mark schemes and example answers to see how each is marked.

1Calculate2 marks

Computers manipulate binary patterns.

Complete the table to show the result of the 8-bit binary addition.

[2 marks]

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

Mark scheme

Award one mark for each correct nibble in the correct order:

1110 (1)
0100 (1)

0 marks if the response is not 8-bit binary.

Example answers and how they were marked

Full marks2/2

1110 0100

Why: 149 + 79 = 228, carrying where a column adds to 2: both nibbles are correct (2).

Some marks1/2

1110 0101

Why: A slip in the last bit. The first nibble is correct (1); the second is not.

No marks0/2

1101 1111

Why: Writes 1 in every column with a 1 and never carries. Neither nibble is correct.

2Calculate2 marks

Binary patterns can represent numbers.

Complete the table to show the result of the 8-bit binary addition.

[2 marks]

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

Mark scheme

Award one mark for each correct nibble in the correct order:

1111 (1)
0010 (1)

0 marks if the response is not 8-bit binary.

Example answers and how they were marked

Full marks2/2

1111 0010

Why: 150 + 92 = 242, carrying where a column adds to 2: both nibbles are correct (2).

Some marks1/2

1111 0011

Why: A slip in the last bit. The first nibble is correct (1); the second is not.

No marks0/2

1101 1110

Why: Writes 1 in every column with a 1 and never carries. Neither nibble is correct.

3Calculate2 marks

Computer systems manipulate bit patterns.

Complete the table to show the result of the 8-bit binary addition.

[2 marks]

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

Mark scheme

Award one mark for each correct nibble in the correct order:

1101 (1)
0111 (1)

0 marks if the response is not 8-bit binary.

Example answers and how they were marked

Full marks2/2

1101 0111

Why: 184 + 31 = 215, carrying where a column adds to 2: both nibbles are correct (2).

Some marks1/2

1010 0111

Why: Writes 0 for 1 + 1 but forgets to carry the 1. The second nibble is correct (1); the first is not.

No marks0/2

1011 1111

Why: Writes 1 in every column with a 1 and never carries. Neither nibble is correct.

4Calculate3 marks

Binary patterns can represent numbers.

(a)

Complete the table to show the 8-bit result of the binary addition.

[2 marks]

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

Mark scheme

Award one mark for each correct nibble in the correct order:

1011 (1)
0111 (1)

0 marks if the response is not 8-bit binary.

Ignore a carry shown beyond the eighth bit.

Example answers and how they were marked

Full marks2/2

1011 0111

Why: 219 + 220 = 439, which needs 9 bits; the 8 bits that are kept are both correct (2).

Some marks1/2

0000 0111

Why: Forgets to carry the 1s. The second nibble is correct (1); the first is not.

No marks0/2

1101 1111

Why: Never carries. Neither nibble is correct.

(b)

State the name of the error that occurs when this addition is carried out.

[1 mark]

Mark scheme

Award one mark for:

overflow (error) (1)

Example answers and how they were marked

Full marks1/1

Overflow

Why: The result needs more bits than are available (1).

No marks0/1

Underflow

Why: A near miss: the result is too big for 8 bits, not too small.

No marks0/1

A syntax error

Why: A syntax error is a mistake in a program's code, not in arithmetic.

5Calculate3 marks

Computers manipulate binary patterns.

(a)

Complete the table to show the 8-bit result of the binary addition.

[2 marks]

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

Mark scheme

Award one mark for each correct nibble in the correct order:

0010 (1)
0100 (1)

0 marks if the response is not 8-bit binary.

Ignore a carry shown beyond the eighth bit.

Example answers and how they were marked

Full marks2/2

0010 0100

Why: 193 + 99 = 292, which needs 9 bits; the 8 bits that are kept are both correct (2).

Some marks1/2

0010 0101

Why: A slip in the last bit. The first nibble is correct (1); the second is not.

No marks0/2

1110 0011

Why: Never carries. Neither nibble is correct.

(b)

State the name of the error that occurs when this addition is carried out.

[1 mark]

Mark scheme

Award one mark for:

overflow (error) (1)

Example answers and how they were marked

Full marks1/1

Overflow

Why: The result needs more bits than are available (1).

No marks0/1

Underflow

Why: A near miss: the result is too big for 8 bits, not too small.

No marks0/1

A syntax error

Why: A syntax error is a mistake in a program's code, not in arithmetic.

6Calculate3 marks

Computers manipulate binary patterns.

(a)

Complete the table to show the 8-bit result of the binary addition.

[2 marks]

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

Mark scheme

Award one mark for each correct nibble in the correct order:

0111 (1)
0101 (1)

0 marks if the response is not 8-bit binary.

Ignore a carry shown beyond the eighth bit.

Example answers and how they were marked

Full marks2/2

0111 0101

Why: 185 + 188 = 373, which needs 9 bits; the 8 bits that are kept are both correct (2).

Some marks1/2

0000 0101

Why: Forgets to carry the 1s. The second nibble is correct (1); the first is not.

No marks0/2

1011 1101

Why: Never carries. Neither nibble is correct.

(b)

State the name of the error that occurs when this addition is carried out.

[1 mark]

Mark scheme

Award one mark for:

overflow (error) (1)

Example answers and how they were marked

Full marks1/1

Overflow

Why: The result needs more bits than are available (1).

No marks0/1

Underflow

Why: A near miss: the result is too big for 8 bits, not too small.

No marks0/1

A syntax error

Why: A syntax error is a mistake in a program's code, not in arithmetic.

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