A decimal number has 25 digits. The number of bits needed for its equivalent binary re is, approximately
Answers
Given : A decimal number has 25 digits.
To Find : The number of bits needed for its equivalent binary representation is, approximately
Solution:
Decimal number has 25 digits
it can be
k x 10²⁴ 1 ≤ k < 10
10²⁴ = (10³ )⁸
10³ ≈ 2¹⁰ 10³ = 1000 , 2¹⁰ = 1024
10²⁴ ≈ (2¹⁰ )⁸
=>10²⁴ ≈ 2⁸⁰
Approximate 81 Digits
other way to cover largest 25 digits number
10²⁵ – 1 = 2ⁿ – 1
=> 10²⁵ = 2ⁿ
=> taking log both sides
=> 25 = nlog2
=> 25 = n(0.301)
=> n ≈ 83
Approx. 83 Digits
80 to 84 bits will almost covers all 25 Digits number
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Step-by-step explanation: