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Suppose the largest n-bit binary number requires ‘d’ digits in decimal representation. Which of the following relation between ‘n’ and 'd’ is approximately correct?
  • a)
    d = 2n
  • b)
    n = 2d
  • c)
    d < n log102
  • d)
    d > n log102
Correct answer is option 'D'. Can you explain this answer?
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Suppose the largest n-bit binary number requires ‘d’ digit...
N bits to represent. This is because a binary number with n bits can have 2^n different values, ranging from 0 to 2^n - 1. Therefore, the largest n-bit binary number is 2^n - 1, which requires n bits to represent.

For example, the largest 4-bit binary number is 1111, which represents 2^4 - 1 = 15 in decimal. Similarly, the largest 8-bit binary number is 11111111, which represents 2^8 - 1 = 255 in decimal.
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Suppose the largest n-bit binary number requires ‘d’ digits in decimal representation. Which of the following relation between ‘n’ and 'd’ is approximately correct?a)d = 2nb)n = 2dc)d < n log102d)d > n log102Correct answer is option 'D'. Can you explain this answer?
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