patternMinor
Balanced based representation
Viewed 0 times
balancedrepresentationbased
Problem
I'm interested in balanced base $B$ representation for fixed point arithmetic. The paper Fixed-point arithmetic in SHE schemes (Costache, Smart, Vivek and Waller, in Proceedings of 23rd International Conference on Selected Areas in Cryptography (SAC 2016), Springer Lecture Notes in Computer Science, vol. 10532, pp. 401–422, 2016; PDF) provides two examples using balanced based $B=3$. However, I don't understand the 2nd second representation, i.e.
$$\frac{8}{3}=10.\bar{1} $$
where $\bar{1}=-1$.
More generally speaking, I'm also interested in balanced form representation $B=5, 7$.
I believe this should be a well-known problem, though I was not able to google it. Do you know some relevant literature to this?
$$\frac{8}{3}=10.\bar{1} $$
where $\bar{1}=-1$.
More generally speaking, I'm also interested in balanced form representation $B=5, 7$.
I believe this should be a well-known problem, though I was not able to google it. Do you know some relevant literature to this?
Solution
The expression $10.\overline{1}$ should be interpreted as follows:
$$
1 \cdot 3^1 + 0 \cdot 3^0 + (-1) \cdot 3^{-1} = 3 - \frac{1}{3} = \frac{8}{3}.
$$
The interpretation of balanced base $b=2d+1$ is the same, with the digits ranging from $-d$ to $d$.
$$
1 \cdot 3^1 + 0 \cdot 3^0 + (-1) \cdot 3^{-1} = 3 - \frac{1}{3} = \frac{8}{3}.
$$
The interpretation of balanced base $b=2d+1$ is the same, with the digits ranging from $-d$ to $d$.
Context
StackExchange Computer Science Q#101404, answer score: 2
Revisions (0)
No revisions yet.