binary conversion using 3 figures system 0,1,2

Question

Suppose system is evolved by extraterrestrial creatures having only 3 figures and they use the figures 0,1,2 with (2>1>0) ,How to represent the binary equivalent of 222 using this?

I calculated it to be 22020 but the book answers it 11010 .how this.Shouldn't i use the same method to binary conversion as from decimal to binary except using '3' here ???

Answer 1

I think you meant base 3 (not binary) equivalent of decimal 222

22020 in base 3 is 222 in decimal.
220202(your answer) in base 3 is 668 in decimal.
11010 (according to book) in base 3 is 111 in decimal.

222 in binary is 11011110

May be i will be able to tell where you went wrong if you tell the method you used to calculate base 3 equivalent of 222

Edit: Sorry I could not understand the problem until you provide the link. It says what is binary equivalent of 222 (remember 222 is in base 3)

222 in base 3 = 26 in decimal (base 10)
26 in decimal = 11010 in binary

Mark it as accepted if it solved your problem.

Answer 2

Assuming the start is decimal 222.

Well, without knowing the system used in the book I would decompose it by hand in the following way:

3^4 = 81,
3^3 = 27,
3^2 = 9,
3^1 = 3,

So 81 fits twize into 222 , so the 4th "bit" has the value 2. Remaining are 60. 27 fits twice into 60 so the next bit is 2 again. Remaining are 6. 9 fits not into 6, so the next bit is 0. Remaining are 6. 3 fits twice into 6, so the next bit is 2. remaining are 0. so the last bit 0

This gives as result 22020.

One quick sanity check on how many "bits" are needed for representation of decimal 222 in a number system with 3 Numbers: 1+log(222)/log(3)=5,9 => nearly 6 "bits" are needed, which goes well with the result 22020.

Answer 3

First see how many figures you have, here we have 3 so we have to convert 222 to binary when we have only 3 figures so

2×3^2+2×3^1+2×3^0 (if the number were being 121 then → 1×3^2+2×3^1+1×3^0)

which gives 26 then divide this with 2 until we don't get 1/2 when reminder is 1 then write 1 if 0 then 0 you will get

so we get 01011 just reverse it we have the answer 11010

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