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A decimal number has 18 digits, The number of bits needed for its equivalent binary representation is(Approximately)?
- a)70
- b)80
- c)60
- d)50
Correct answer is option 'C'. Can you explain this answer?
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A decimal number has 18 digits, The number of bits needed for its equ...
Maximum number using 18 digits = 1018-1
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1018-1= 2n
Take log both side
log10(1018-1) = log10(2n)
~ log10(1018) = log10(2n)
18 = n log102
n = 18/ log102
n = 59.79
~ n = 60
Most Upvoted Answer
A decimal number has 18 digits, The number of bits needed for its equ...
Understanding Decimal to Binary Conversion
To determine the number of bits required for the binary representation of an 18-digit decimal number, we need to understand the relationship between decimal and binary systems.
Decimal to Binary Conversion Basics
- A decimal number is expressed in base 10, using digits from 0 to 9.
- A binary number is expressed in base 2, using only digits 0 and 1.
Calculating the Maximum Value of an 18-Digit Decimal Number
- The maximum value of an 18-digit decimal number is 999,999,999,999,999,999, which can be approximated as 10^18.
Converting Decimal to Binary
- To find out how many bits are needed for binary representation, we can use the formula:
Number of bits = floor(log2(max decimal number)) + 1
- For our maximum decimal number, we have:
log2(10^18) = 18 * log2(10)
- Using the approximation log2(10) ≈ 3.32193, we find:
log2(10^18) ≈ 18 * 3.32193 ≈ 59.79
Final Calculation
- Rounding up, we get:
Number of bits ≈ 59.79 + 1 ≈ 60.79
- Therefore, the number of bits needed is approximately 60.
Conclusion
- The correct answer is option 'C', as about 60 bits are required to represent an 18-digit decimal number in binary.
To determine the number of bits required for the binary representation of an 18-digit decimal number, we need to understand the relationship between decimal and binary systems.
Decimal to Binary Conversion Basics
- A decimal number is expressed in base 10, using digits from 0 to 9.
- A binary number is expressed in base 2, using only digits 0 and 1.
Calculating the Maximum Value of an 18-Digit Decimal Number
- The maximum value of an 18-digit decimal number is 999,999,999,999,999,999, which can be approximated as 10^18.
Converting Decimal to Binary
- To find out how many bits are needed for binary representation, we can use the formula:
Number of bits = floor(log2(max decimal number)) + 1
- For our maximum decimal number, we have:
log2(10^18) = 18 * log2(10)
- Using the approximation log2(10) ≈ 3.32193, we find:
log2(10^18) ≈ 18 * 3.32193 ≈ 59.79
Final Calculation
- Rounding up, we get:
Number of bits ≈ 59.79 + 1 ≈ 60.79
- Therefore, the number of bits needed is approximately 60.
Conclusion
- The correct answer is option 'C', as about 60 bits are required to represent an 18-digit decimal number in binary.
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A decimal number has 18 digits, The number of bits needed for its equivalent binary representation is(Approximately)?a)70b)80c)60d)50Correct answer is option 'C'. Can you explain this answer?
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