How many bits are required to count upto decimal 1 million?

Question

Programming ...

How can we find numbers of bit of a number

Answer 1

Hint: one million = 10⁶ = 2^x

Taking common (base 10) logs, 6 = x(log 2)

6 = x(0.30103)

x = 6/0.30103) = 19.93, approximately

 

So one million is a bit less than 2²⁰ which means it would fit in 20 bits.

 

This is reasonable since 16,777,216 is 2²⁴ -- a fact that I memorized in April 1964 when the maximum memory address of System 360 was announced.