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

Practice Questions

Q1
In a base-5 number system, what is the sum of '23' and '14'?
  1. 42
  2. 32
  3. 41
  4. 30

Questions & Step-by-Step Solutions

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'.
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