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In a base-8 system, what is the value of the number 345 (base 8) in base-10?
- a)229
- b)228
- c)230
- d)231
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a base-8 system, what is the value of the number 345 (base 8) in ba...
Understanding Base-8 (Octal) Number System
The base-8, or octal, number system uses digits from 0 to 7. Each digit's position represents a power of 8, similar to how the decimal system (base-10) uses powers of 10.
Converting 345 (base 8) to Base-10
To convert the octal number 345 to decimal (base-10), we evaluate each digit based on its position:
- The rightmost digit (5) is in the 8^0 position.
- The middle digit (4) is in the 8^1 position.
- The leftmost digit (3) is in the 8^2 position.
Calculation Steps
- Breakdown of the value:
- 3 × 8^2 = 3 × 64 = 192
- 4 × 8^1 = 4 × 8 = 32
- 5 × 8^0 = 5 × 1 = 5
- Adding these values together:
- Total = 192 + 32 + 5
Final Calculation
- Total = 229
Conclusion
Thus, the decimal equivalent of the octal number 345 is 229, confirming that the correct answer is option 'A'. This conversion process illustrates how to translate numbers between different bases, providing a solid understanding of the base-8 system.
The base-8, or octal, number system uses digits from 0 to 7. Each digit's position represents a power of 8, similar to how the decimal system (base-10) uses powers of 10.
Converting 345 (base 8) to Base-10
To convert the octal number 345 to decimal (base-10), we evaluate each digit based on its position:
- The rightmost digit (5) is in the 8^0 position.
- The middle digit (4) is in the 8^1 position.
- The leftmost digit (3) is in the 8^2 position.
Calculation Steps
- Breakdown of the value:
- 3 × 8^2 = 3 × 64 = 192
- 4 × 8^1 = 4 × 8 = 32
- 5 × 8^0 = 5 × 1 = 5
- Adding these values together:
- Total = 192 + 32 + 5
Final Calculation
- Total = 229
Conclusion
Thus, the decimal equivalent of the octal number 345 is 229, confirming that the correct answer is option 'A'. This conversion process illustrates how to translate numbers between different bases, providing a solid understanding of the base-8 system.
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In a base-8 system, what is the value of the number 345 (base 8) in ba...
Solution:
To convert the number 345 from base-8 to base-10, follow these steps:
- Identify the place values in base-8:
- 3 in the hundreds place (8²)
- 4 in the tens place (8¹)
- 5 in the units place (8⁰)
- Calculate the value of each digit:
- 3 × 8² = 3 × 64 = 192
- 4 × 8¹ = 4 × 8 = 32
- 5 × 8⁰ = 5 × 1 = 5
- Add these values together:
- 192 + 32 + 5 = 229
Thus, the value of 345 in base-10 is 229.
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