How many bit are needed to represent 32 digit decimal number?

Question

A large number, 32 digit decimal number is given. How many bit are needed to represent in binary ?

Are you familiar with how logarithms relate to the number of digits of a number in a particular base? This is a straightforward application of that fact. — JMoravitz, Jun 28 '19 at 14:12
number of digits is one more than greatest integer of logarithm — J. W. Tanner, Jun 28 '19 at 14:15
Answer: 107 bits $$\left\lceil \log_2 99,999,999,999,999,999,999,999,999,999,999 \right\rceil = 107$$ — SlipEternal, Jun 28 '19 at 14:23
Possible duplicate of How many bits needed to store a number — JMoravitz, Jun 28 '19 at 14:32
@InterstellarProbe floor and add one instead of using ceiling. Otherwise you'll run into errors when asking about powers of two. $\lceil\log_2(4)\rceil = 2$ but $4$ is represented as $100_2$ in binary requiring three digits, not $2$. — JMoravitz, Jun 28 '19 at 14:40
The number of base-$b$ digits to represent $n$ is $1+\lfloor\log_b(n)\rfloor$. — robjohn, Jun 28 '19 at 14:41

score 2 · Answer 1 · answered Jun 28 '19 at 14:16

2

Hint:

$2\leq\log_2(4)<\log_2(7)<3\leq\log_2(8)<\log_2(15)<4$

answered Jun 28 '19 at 14:16

JMoravitz

2

Maybe too abstract for the OP, he seems clueless about logarithms – gt6989b Jun 28 '19 at 14:26
1

you could have said $2=\log_24$ and $3=\log_2(8)$ – J. W. Tanner Jun 28 '19 at 14:53

1 Answers1