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What is the sum of the numbers '12' and '21' in base-3?
What is the sum of the numbers '12' and '21' in base-3?
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Q1
What is the sum of the numbers '12' and '21' in base-3?
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'12' in base-3 is 3 and '21' is 7. Their sum is 10, which is '100' in base-3.
Questions & Step-by-step Solutions
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Q
Q: What is the sum of the numbers '12' and '21' in base-3?
Solution:
'12' in base-3 is 3 and '21' is 7. Their sum is 10, which is '100' in base-3.
Steps: 10
Show Steps
Step 1: Understand that '12' in base-3 means 1*3^1 + 2*3^0.
Step 2: Calculate '12' in base-3: 1*3 + 2*1 = 3 + 2 = 5.
Step 3: Understand that '21' in base-3 means 2*3^1 + 1*3^0.
Step 4: Calculate '21' in base-3: 2*3 + 1*1 = 6 + 1 = 7.
Step 5: Add the two results: 5 + 7 = 12.
Step 6: Convert the sum (12) back to base-3.
Step 7: To convert 12 to base-3, divide by 3: 12 ÷ 3 = 4 (remainder 0).
Step 8: Divide 4 by 3: 4 ÷ 3 = 1 (remainder 1).
Step 9: Divide 1 by 3: 1 ÷ 3 = 0 (remainder 1).
Step 10: Read the remainders from bottom to top: 110 in base-3.
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