search
Log In
1 vote
1.6k views

A computer uses ternary system instead of the traditional systen, An $n$ bit string in the binary system will occupy

  1. $3+n$ ternary digits
  2. $2n/3$ ternary digits
  3. $n$$\log_{2}3$ ternary digits
  4. $n$$\log_{3}2$ ternary digits
in CO and Architecture
recategorized by
1.6k views

3 Answers

8 votes
 
Best answer

Let the no. of digits occupied by the ternary system be 'x'

Now,Maxi. value representable in ternary system using x digits = Maxi. value representable in binary system using  n digits

3x-1=2n-1

x=log32n = n log32   (d)


selected by
13 votes

Maximum No. possible using n-bit in Binary:- 2n -1

Maximum no. possible using x bit in Ternary:- 3x -1

Both will take different no. of bits to represent same number. 

3x -1 =  2n -1

3=  2n

taking log on both side:;-

X= log3 ( 2 )

X=n*log32 .

0
@Sonveer tomar 1,Could you elaborate how you've got 3 in base of log?What property you've used?
1

For example:-

10n = 1000. For what value of n we get this

take log base 10 on both side.

log(10n ) = log(1000)

n log(10) = 3* log(10)

n=3.

In same manner to find value of X i take log base 3 on both side

0
@Sonveer tomar 1,Thank you so much for the explanation. :)
0
can you please elaborate, what question want to ask???
1

the problem is simply trying to ask---> given an n-bit binary number howmany digits that that it would be required to represent that number in ternary number system....so here we try to find howmany number of digits in ternary number system that will be required to represent the maximum valued n-bit binary number......

so,let x digits required in ternary number system to represent the maximum valued n-bit binary number which is (2^n-1)(in decimal)....and maximum valued decimal number with x digit in ternary number system will be (3^x-1)...

so ,(2^n-1)<=(3^x-1)

     =>  2^n<=3^x

     =>  x>=nlog2base3

 

3 votes
D is correct
Answer:

Related questions

3 votes
5 answers
1
3.4k views
If a variable can take only integral values from $0$ to $n$, where $n$ is an integer, then the variable can be represented as a bit-field whose width is $($the log in the answer are to the base $2$, and $\left \lceil \log_{}{n} \right \rceil$ ... $\left \lceil \log (n+1) \right \rceil + 1\text{ bits}$ None of the above
asked Apr 22, 2018 in Digital Logic Arjun 3.4k views
1 vote
4 answers
2
1.5k views
Given $\sqrt{224_{r}}$= $13$_{r}$ the value of radix $r$ is $10$ $8$ $6$ $5$
asked Apr 22, 2018 in Digital Logic Arjun 1.5k views
2 votes
3 answers
3
1.7k views
A data driven machine is one that executes an instruction if the needed data is available. The physical ordering of the code listing does not dictate the course of execution. Consider the following pseudo-code: Multiply $E$ by $0.5$ to get $F$ Add $A$ and $B$ to get $E$ Add $B$ with $0.5$ ... sequence of execution is valid? B, C, D, A, E C, B, E, A, D A, B, C, D, E E, D, C, B, A
asked Apr 22, 2018 in CO and Architecture Arjun 1.7k views
1 vote
4 answers
4
1.7k views
A byte addressable computer has a memory capacity of $2$^{m}$KB$ ($k$ bytes) and can perform $2$^{n}$ operations. An instruction involving $3$ operands and one operator needs maximum of: $3m$ bits $3m + n$ bits $m + n$ bits none of the above
asked Apr 22, 2018 in CO and Architecture Arjun 1.7k views
...