In a base-5 number system, what is the sum of '23' and '14'?

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Question: In a base-5 number system, what is the sum of \'23\' and \'14\'?

Options:

Correct Answer: 42

Solution:

In base-5, \'23\' is 2*5 + 3 = 13 and \'14\' is 1*5 + 4 = 9. Their sum is 22 in decimal, which is \'42\' in base-5.

In a base-5 number system, what is the sum of '23' and '14'?

In a base-5 number system, what is the sum of '23' and '14'?

Step 1: Understand that we are working in base-5. This means each digit represents a power of 5.
Step 2: Convert '23' from base-5 to decimal. Calculate 2*5^1 + 3*5^0 = 2*5 + 3*1 = 10 + 3 = 13.
Step 3: Convert '14' from base-5 to decimal. Calculate 1*5^1 + 4*5^0 = 1*5 + 4*1 = 5 + 4 = 9.
Step 4: Add the two decimal numbers together: 13 + 9 = 22.
Step 5: Convert the sum (22) back to base-5. Divide 22 by 5. The quotient is 4 and the remainder is 2. So, 22 in base-5 is '42'.

Base Conversion – Understanding how to convert numbers from base-5 to decimal and vice versa.
Addition in Non-Decimal Bases – Performing addition operations within a number system that is not base-10.