Binary addition rules

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Quick Questions

Shade in the A or B circle for each question.

1. In binary, what is 1 + 1?

A 10 (write 0, carry 1)

B 2 (write 2 in the column)

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

A 1 with no carry

B 10 with a carry of 1

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

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

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)

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
11 + 1 = 10		AThe digit 2 does not exist in binary. 1 + 1 should be written as 10 (write 0, carry 1).
21 + 1 + 1 = 11		BIn binary, adding two 1s gives 0 in this column and carries 1 into the next column
3A column with 1 + 1 and no carry in: write 0 and carry 1 to the next column		C0 + 1 = 1
4A column with 0 + 1 and no carry in: write 1 and carry nothing		DAdding a carry digit to two 1s gives 1 in this column and carries 1 into the next column
51 + 1 = 2		EThree 1s make 3 in denary, which is 11 in binary. Write 1 and carry 1, not 0 and carry 1.
61 + 1 + 1 = 10		F1 + 1 = 10

Definitions

1+1=10

Fill in the Blanks

Complete each line of code by filling in the missing parts.

0+1=_

1+1=__

1+1+1=__

1+1=10: write _ and carry 1

011 + 011 = ___

Spot the Error

Shade in the letter of the line that contains an 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)

Question 2

A 1 + 1 = 11 in binary

B Write 0 in this column

C Carry 1 to the next column

Question 3

A 0101

B + 0011

C = 0110

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

Question 5

A 0 + 1 = 10

B 1 + 0 = 1

C 0 + 0 = 0

Answer Key

Binary addition rules

Section A: Quick Questions

A — 10 (write 0, carry 1)

A — 1 with no carry

A — Write 0, carry 1

B — Into the next column on the left

B — 11 (write 1, carry 1)

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

0+1=1

1+1=10

1+1+1=11

1+1=10: write 0 and carry 1

  011
+ 011
= 110

Section E: Spot the Error

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).

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.

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.

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.

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