"_3" represents the base 3

Consider a hypothetical computer which supports a ternary (or base-3) number system. In representation, the digits used to form a base-3 number are only 0, 1 and 2. For example, obviously we have (10 101)3 and (100)1 10201)3 for unsigned numbers In order to also support signed numbers, your task is to apply the idea of two's complement in binary representations to design a three's complement scheme for n-digits signed ternary numbers (only for negative numbers), so that we can also reuse the adder unit in ALU for subtraction. You should give an encoding rule just like the "flip-bits-plus-one" rule for two's complement. Then calculate the range of numbers that can be represented by this scheme if n 4 12 (Hint: Starting with a similar mathematical property like two's complement; the sign digit is still the most significant one, but both 0 and 1 can be for a positive value and both 1 and 2 can indicate a negative value.) This question is totally follows the idea of 2's complement for binary Here is a 2 digits example (1) for unsigned value, we can represent 0-8 with base-3, they are 0 (00)3, 1-(01)_3, 2-(02)_3, 3-(10)_3, 4-(11)3 5 (12) 3, 6-(20)_3, 7-(21) 3, 8-(22)_3 (2) to make a 3's complement, the representations of K and -K should meet: (K) 3+(-K) 3-(00)_3+Carry-(100) 3-9 So, we know (-K)_3 shares the same representation with (9-K) 3 (unsigned). That is 1-(22)3, -2 (21) 3, -3- (20_3, -4 (12) 3 (3) compare the following data, what pattern do you find? 0 (00)3, 1- (01)_3, 2- (02)_3, 3 (10) 3, 4-(11) 3, 1 (22)3, -2- (21) 3, -3- (20) 3, -4 (12)3 So, how will you design the conversion rule? (4) The range? Obviously, here it is -4-4. Follow this idea for 4-digit data