Question

Base 3 System You have invented a technology that enables the efficient implementation of a trinary (3 state) system. The company to which you've sold your invention, TriState Corp., has asked you to design a base-3 floating-point system that is at least as accurate as an IEEE binary32 binary floating- point system. How many digits would you propose for your system? You should discuss the reasons behind your proposal.

Answer 1

IEEE floating point number has the following part:

1-bit sign:

No change since there is only positive or negative, in ternary system we can asign one to positive , one to negative and other useless.

8-bit biased exponent:

The IEEE exponent can represent 256 exponent values

if we choose 6 bits we can represent 729 exponent values in ternary system, but if we choose 5 it gives only 243 < 256

Normalised Mantissa:

The mantissa uses 23bits+1implicit bit = 24 bits to represent the mantissa which can represent upto 2^24 values

to get atleast that much precision we need to choose,

> loga(224)24log32 15.14 m

Hence we will choose m = 16. Here we cannot have a implicit bit because we can have two values other than zero which need to be differntiated

Hence Number of bits neeeded = 1+6+16 = 23