ExpertMedium2 marksShort Answer
AQA GCSE · Question 02.1 · Fundamentals of data representation
Add together the following three binary numbers and give your answer in binary.
00110110
10010010
- 00100001
Add together the following three binary numbers and give your answer in binary.
00110110
10010010
- 00100001
How to approach this question
To add binary numbers, work from right to left, column by column, following these rules:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, carry 1
1 + 1 + 1 = 1, carry 1
00110110
10010010
+ 00100001
----------
11101001
Column 1 (rightmost): 0 + 0 + 1 = 1
Column 2: 1 + 1 + 0 = 0, carry 1
Column 3: 1 + 0 + 0 + (carry 1) = 0, carry 1
Column 4: 0 + 0 + 0 + (carry 1) = 1
Column 5: 1 + 1 + 0 = 0, carry 1
Column 6: 1 + 0 + 1 + (carry 1) = 1, carry 1
Column 7: 0 + 0 + 0 + (carry 1) = 1
Column 8: 0 + 1 + 0 = 1
Full Answer
11101001
Binary addition follows specific rules. Let's add the three numbers column by column from right to left.
(carry) 111 1
00110110
10010010
+ 00100001
----------------
11101001
- **Column 1 (2^0):** 0 + 0 + 1 = 1.
- **Column 2 (2^1):** 1 + 1 + 0 = 10 (binary). Write down 0, carry over 1.
- **Column 3 (2^2):** 1 + 0 + 0 + (carry 1) = 10 (binary). Write down 0, carry over 1.
- **Column 4 (2^3):** 0 + 0 + 0 + (carry 1) = 1.
- **Column 5 (2^4):** 1 + 1 + 0 = 10 (binary). Write down 0, carry over 1.
- **Column 6 (2^5):** 1 + 0 + 1 + (carry 1) = 11 (binary). Write down 1, carry over 1.
- **Column 7 (2^6):** 0 + 0 + 0 + (carry 1) = 1.
- **Column 8 (2^7):** 0 + 1 + 0 = 1.
The final answer is 11101001.
Common mistakes
✗ Forgetting to carry over when the sum of a column is 2 or more.
✗ Making simple arithmetic errors.
✗ Adding the numbers as if they were decimal.
Practice the full AQA GCSE Computer Science Paper 2
46 questions · hints · full answers · grading
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