← IGCSE Computer Science Paper 1

Binary addition rules

Binary addition rules: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1) and 1+1+1=11 (write 1, carry 1). Add column by column, carrying into the next column.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 21, IGCSE Computer Science 0478 — 2.2 Methods of Error Detection — Module 22

Understanding Binary addition rules in IGCSE Computer Science Paper 1

What it does: The answer 10 shows the 0 to write and the 1 to carry. The total is less than 2, so there is no carry and the answer is just 1. Binary only has the digits 0 and 1, so 1 + 1 = 10. You write 0 in the column and carry 1 into the next column. Column values increase towards the left, so a carry always moves one column to the left, just like in denary addition. 0 + 0 = 0. Nothing is carried because the column total is 0. The carry digit is added like any other digit, so 0 + 1 + carry 1 is 1 + 1 = 10. Write 0 and carry 1 again.

Common mistakes: 1 + 1 = 10 in binary, so you write 0 in the column and carry 1 to the next column. It should say (write 0, carry 1). 1 + 1 equals 10 in binary (two), not 11. 11 is the result of 1 + 1 + 1. The line should be 1 + 1 = 10 in binary.

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Learning

Duo

In binary, what is 1 + 1?

2 (write 2 in the column)10 (write 0, carry 1)

Matches

1 + 1 = 2

↓

The digit 2 does not exist in binary. 1 + 1 should be written as 10 (write 0, carry 1).

Applying

Meanings

Term

1+1=10

Meaning

Binary addition rules: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1) and 1+1+1=11 (write 1, carry 1). Add column by column, carrying into the next column.

Practice

0+0=0

Testing

Gaps

0+1=

Check Answer

Spots

20 + 1 = 1

31 + 1 = 10 (write 1, carry 0)

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Quick Questions

1. In binary, what is 1 + 1?

A. 10 (write 0, carry 1) ✓

B. 2 (write 2 in the column)

Binary only has the digits 0 and 1, so 1 + 1 = 10. You write 0 in the column and carry 1 into the next column.

2. Which is the correct result of 0 + 1 in binary?

A. 1 with no carry ✓

B. 10 with a carry of 1

0 + 1 = 1. There is no carry because the answer fits in a single binary digit.

3. A column adds 1 + 1 and there is no carry in. What do you write and carry?

A. Write 0, carry 1 ✓

B. Write 1, carry 1

1 + 1 = 10 in binary, so you write the 0 and carry the 1 to the next column on the left.

4. Where does the carry digit go after a column gives 1 + 1 = 10?

A. Into the next column on the right

B. Into the next column on the left ✓

Column values increase towards the left, so a carry always moves one column to the left, just like in denary addition.

5. A column has 1 + 1 + 1 (two 1s plus a carry in). What is the result?

A. 10 (write 0, carry 1)

B. 11 (write 1, carry 1) ✓

1 + 1 + 1 = 3 in denary, which is 11 in binary. Write 1 in the column and carry 1 to the next column.

Match the Pairs

1 + 1 = 10 → In binary, adding two 1s gives 0 in this column and carries 1 into the next column

1 + 1 + 1 = 11 → Adding a carry digit to two 1s gives 1 in this column and carries 1 into the next column

A column with 1 + 1 and no carry in: write 0 and carry 1 to the next column → 1 + 1 = 10

A column with 0 + 1 and no carry in: write 1 and carry nothing → 0 + 1 = 1

1 + 1 = 2 → The digit 2 does not exist in binary. 1 + 1 should be written as 10 (write 0, carry 1).

1 + 1 + 1 = 10 → Three 1s make 3 in denary, which is 11 in binary. Write 1 and carry 1, not 0 and carry 1.

Key Term

1+1=10

Binary addition rules: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1) and 1+1+1=11 (write 1, carry 1). Add column by column, carrying into the next column.

Fill in the Blanks

1. 0+1=1

Hint: Type the single digit you get when you add 0 and 1 in binary.

2. 1+1=10

Hint: Type the two-digit binary result of adding two 1s.

3. 1+1+1=11

Hint: Type the two-digit binary result of adding three 1s (two 1s plus a carry).

4. 1+1=10: write 0 and carry 1

Hint: Type the digit that is written in the current column.

5. 011 + 011 = 110

Hint: Type the binary total, remembering to carry into the next column.

Spot the Error

Question 1

A 0 + 0 = 0

B 0 + 1 = 1

C 1 + 1 = 10 (write 1, carry 0)

D 1+1+1 = 11 (write 1, carry 1)

Line C — 1 + 1 = 10 in binary, so you write 0 in the column and carry 1 to the next column. It should say (write 0, carry 1).

Question 2

A 1 + 1 = 11 in binary

B Write 0 in this column

C Carry 1 to the next column

Line A — 1 + 1 equals 10 in binary (two), not 11. 11 is the result of 1 + 1 + 1. The line should be 1 + 1 = 10 in binary.

Question 3

A 0101

B + 0011

C = 0110

Line C — The carries were forgotten. 0101 + 0011 gives 1000: each of the three right columns makes 1 + 1 = 10, writing 0 and carrying 1, and the last carry becomes the leading 1.

Question 4

A Column 1: 1 + 1 = 10, carry 1

B Column 2: 1 + 1 + carry 1

C 1+1+1 = 11: write 0, carry 1

Line C — 1 + 1 + 1 = 11, so you write 1 in the column and carry 1. Writing 0 is the rule for 1 + 1 = 10, not for adding a carry to two 1s.

Question 5

A 0 + 1 = 10

B 1 + 0 = 1

C 0 + 0 = 0

Line A — 0 + 1 = 1 in binary. There is no carry because the total fits in one bit. Only 1 + 1 gives 10.

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