How to convert a number from decimal to balanced ternary?

Question

Python

Hello! Help solve the problem, please. Please explain how exactly to transfer.

Answer 1

1) Convert the number to the "ordinary" ternary number system - and if the number is negative, then add a minus to all digits
2) go through the digits from right to left: replace all (2) with ($) and add +1 to the higher digit; we replace all (3) with (0) and add (+1) to a higher digit; we replace all (-2) with (1) and add (-1) to a higher digit; we replace all (-3) with 0 and add (-1) to the higher bit.
"Positive" example : 71 (underscore means loop counter location)

71 = 27*2 + 9*1 + 3*2 + 1*2
   2 1 2 2<
   2 1 3<$
   2 2<0 $
   3<$ 0 $
 1<0 $ 0 $
<1 0 $ 0 $

Checking: 81 - 9*1 - 1 = 71
"Negative" example: -71

-71 = 27*(-2) + 9*(-1) + 3*(-2) + 1*(-2)
   -2 -1 -2 -2<
   -2 -1 -3< 1
   -2 -2< 0  1
   -3< 1  0  1
 $< 0  1  0  1
<$  0  1  0  1

Checking: 81*(-1) + 9*1 + 1*1 = -71

Answer 2

In fact, the following negative unit sign is adopted: ͞1. Brusentsov also wrote this. And it's easy to translate. An asymmetric ternary system can be converted into a symmetrical one by setting: 2 → 1͞1. That is, we translate the number 7 as 21, and then arithmetically as 1͞10 + 001 = 1͞11. Let's take the number 14 as an example and translate it into a symmetrical and balanced system. We get the number 14 in the asymmetric system as 112, then we get the following: 110 + 01͞1 = 1͞1͞1͞1. Or 17 is 122 in asymmetrical or 1͞10͞1 in symmetrical. For negative it is implemented very simply. First we reserve a negative value. Let's transform the number as positive, and at the end of the series of trits, we will invert it due to the negative sign. For example: -17 is ͞1111. This is how it is decided.