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In a base-3 system, what is the sum of the base-3 numbers 12 and 21?

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Question: In a base-3 system, what is the sum of the base-3 numbers 12 and 21?

Options:

  1. 110
  2. 100
  3. 102
  4. 111

Correct Answer: 110

Solution: 

To add in base-3, convert to decimal: 12 (base-3) = 3 + 2 = 5 (decimal) and 21 (base-3) = 2 + 0 = 2 (decimal). The sum is 5 + 2 = 7 (decimal), which is 21 in base-3.

In a base-3 system, what is the sum of the base-3 numbers 12 and 21?

Practice Questions

Q1
In a base-3 system, what is the sum of the base-3 numbers 12 and 21?
  1. 110
  2. 100
  3. 102
  4. 111

Questions & Step-by-Step Solutions

In a base-3 system, what is the sum of the base-3 numbers 12 and 21?
  • Step 1: Understand that we are working in base-3, which uses the digits 0, 1, and 2.
  • Step 2: Convert the base-3 number '12' to decimal. In base-3, '12' means 1*3^1 + 2*3^0 = 3 + 2 = 5 in decimal.
  • Step 3: Convert the base-3 number '21' to decimal. In base-3, '21' means 2*3^1 + 1*3^0 = 6 + 1 = 7 in decimal.
  • Step 4: Add the two decimal numbers together: 5 + 7 = 12 in decimal.
  • Step 5: Convert the decimal sum (12) back to base-3. To do this, divide 12 by 3: 12 ÷ 3 = 4 (remainder 0), then 4 ÷ 3 = 1 (remainder 1), and finally 1 ÷ 3 = 0 (remainder 1).
  • Step 6: Write the remainders in reverse order to get the base-3 representation: 110.
  • Step 7: Therefore, the sum of the base-3 numbers '12' and '21' is '110' in base-3.
  • Base Conversion – Understanding how to convert numbers from base-3 to decimal and vice versa.
  • Base Addition – Performing addition in a non-decimal base system.
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