Unacadmey book

Question

In a number system range of numbers are - 3to3 represented as C,B ,A,0,1,2,3 what will be 102 base 10 in the system?

Answer 1

Here $-3$ to $3$ are the digits, with corresponding values $-3 = C, -2=B, -1=A, 0, 1, 2$ and $3.$ Then we will have to find values which satisfy the equation:
$d_1 + 7{d_2}+49d_3+343d_4+…. = 102$, where $d_1,d_2…$ are from $\{-3,-2,-1,0,1,2,3\}$. Then we will get $d_1 = -3,
d_2 = 1, d_3=2 $ and $ d_4 =0.$

That is $21(-3)$, which is $21C$ in the given system.