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