Question

it can be shown that every integer can be uniquelyrepresented in the form of
where =-1,0,or 1 for j=0,1,2,...,k
expansion of this type are called balanced ternary expansion.
find balanced ternary expansion of
a)5 b)13 c)37 d)79

Answer 1

a. $5_{10}=1(-1)(-1)_{\mathrm{bal}3}$ because

5 = 9 - 3 - 1 = 3^2 - 3^1 - 3^0

b. $13_{10}=111_{\mathrm{bal}3}$ because

13 = 9 + 3 + 1 = 3^2 + 3^1 + 3^0

c. $37_{10}=1101_{\mathrm{bal}3}$ because

37 = 27 + 9 + 1 = 3^3 + 3^2 + 3^0

d. $79_{10}=100(-1)1_{\mathrm{bal}3}$ because

79 = 81 - 3 + 1 = 3^4 - 3^1 + 3^0