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?
110
100
102
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.
