Binary and addition
Binary Addition Practice with Answers
Add these bit by bit. Start at the rightmost column, write each column's sum, and pass any carry to the column on the left. Finish the problems before you look at the answers.
Problems with no carry
In the first four problems, each column has at most one 1, so you can write each column's result straight down. Afterwards, convert both numbers to decimal and check the sum.
Work out 0001₂ + 0010₂.
Answer
The answer is 0011₂. Decimal check: 1+2=3. No carries; write each column's sum directly.
Work out 0100₂ + 0011₂.
Answer
The answer is 0111₂. Decimal check: 4+3=7. No carries; each column has at most one 1.
Work out 1000₂ + 0101₂.
Answer
The answer is 1101₂. Decimal check: 8+5=13. No carries.
Work out 1010₂ + 0101₂.
Answer
The answer is 1111₂. Decimal check: 10+5=15. No carries; the 1s in the two numbers never line up.
Problems with one carry
The middle four problems each have one column with 1+1. Write 0 in that column, carry 1 to the left, and remember to add that carry in the next column.
Work out 0001₂ + 0001₂.
Answer
The answer is 0010₂. Decimal check: 1+1=2. Lowest column 1+1 writes 0 and carries 1; column 2 gets the carry and writes 1.
Work out 0010₂ + 0010₂.
Answer
The answer is 0100₂. Decimal check: 2+2=4. Column 2 has 1+1, writes 0 and carries 1; column 3 gets the carry and writes 1.
Work out 0101₂ + 0001₂.
Answer
The answer is 0110₂. Decimal check: 5+1=6. Lowest column 1+1 writes 0 and carries 1; column 2 has 0+0+1 and writes 1.
Work out 1001₂ + 0001₂.
Answer
The answer is 1010₂. Decimal check: 9+1=10. Lowest column 1+1 writes 0 and carries 1; column 2 has 0+0+1 and writes 1.
Problems with chain carries
In the last four problems, the carry moves left column after column. After each column, check for a carry before moving on. If the top column still carries, write an extra digit; do not cut it off.
Work out 0011₂ + 0001₂.
Answer
The answer is 0100₂. Decimal check: 3+1=4. The lowest two columns both carry; column 3 has 0+0+1 and writes 1.
Work out 0111₂ + 0001₂.
Answer
The answer is 1000₂. Decimal check: 7+1=8. The carry passes through the lowest three columns; column 4 has 0+0+1 and writes 1.
Work out 1111₂ + 0001₂.
Answer
The answer is 10000₂. Decimal check: 15+1=16. All four columns write 0 and carry; the final carry becomes a fifth bit and must be kept.
Work out 1111₂ + 1111₂.
Answer
The answer is 11110₂. Decimal check: 15+15=30. Lowest column 1+1 writes 0 and carries 1; the other three columns are 1+1+1, writing 1 and carrying 1; the final carry becomes a fifth bit.