Question

How many bits are approximately required to represent a positive integer of base 10 consisting of 25 digits without any leading zeros in binary re?

Answer 1

Answer:

Approx 83 bits are required

Explanation:

How many bits are approximately required to represent a positive integer of base 10 consisting of 25 digits without any leading zeros in binary ?

a positive integer of base 10 consisting of 25 digits

Base 10 = decimal

25 digits largest number  25times 9

9999999999999999999999999

= 10²⁵ - 1

n bits can represent data till 2ⁿ - 1

2ⁿ - 1 ≥ 10²⁵ - 1

=> 2ⁿ  ≥ 10²⁵

Taking log both sides

n Log 2  = 25 Log 10

=> n (0.301) = 25

=> n = 83

Approx 83 bits are required

Answer 2

Answer:

84 bits required

Explanation:

(10^25/2^n)<=1

log(10^25)-n*log(2)<=0

25<=n*log(2)

n>=83.04

min value of n = 84