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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'?
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Q1
In a base-5 number system, what is the sum of '23' and '14'?
42
32
41
30
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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.
Questions & Step-by-step Solutions
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Q
Q: In a base-5 number system, what is the sum of '23' and '14'?
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.
Steps: 5
Show Steps
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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