In a base-4 system, what is the sum of the numbers 3 and 2?

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Question: In a base-4 system, what is the sum of the numbers 3 and 2?

Options:

Correct Answer: 11

Solution:

In base-4, the sum of 3 and 2 is 11 (3 + 2 = 5 in decimal, which is 11 in base-4).

In a base-4 system, what is the sum of the numbers 3 and 2?

In a base-4 system, what is the sum of the numbers 3 and 2?

Step 1: Understand that we are working in a base-4 system, which means the digits can only be 0, 1, 2, or 3.
Step 2: Identify the numbers we want to add: 3 and 2.
Step 3: Add the numbers together in decimal: 3 + 2 = 5.
Step 4: Convert the decimal result (5) into base-4.
Step 5: To convert 5 to base-4, divide 5 by 4. The quotient is 1 and the remainder is 1.
Step 6: Write down the quotient (1) and the remainder (1) to form the base-4 number: 11.
Step 7: Therefore, the sum of 3 and 2 in base-4 is 11.

Base-4 Number System – Understanding how to perform arithmetic operations in a non-decimal base, specifically base-4.
Conversion Between Bases – Converting numbers from decimal to another base and vice versa.