# A number of question & solutions about data and data rates

This is more along the lines of computer driven word questions, but figured my best bet for asisstance would be the Math section. That is why it is being posted here.

Answer ONLY 5 of the questions attached for 6 custom credits.

Pick any 5

#### Solution Preview

(1)

Sociologists can get three possible answers to a typical survey question such as "Do you believe in the tooth fairy?" -namely, yes, no, and no opinion. With this in mind, the Sociomagnetic Computer Company has decided to build a computer to process survey data. This computer has a trinanry of memory-that is, each byte (tryte?) consists of 8 trits, with a trit holding a 0, 1, or 2. How many trits are needed to hold a 6-bit number? Give an expression for the number or trits needed to hold n bits.

A 6 bit number has 26 = 64 possible combinations

As a trit consists of 3 states 0,1 or 2 so we need to use modular 3 arithmetic to determine how many trits (N) are required to store any 6 bit number

We therefore need to solve the equation

3^N >= 64 (1)

Taking Logs to base 10 each side of (1) we get

Log{3}^N >= Log{64}

N*Log{3} >= Log{64}

N >= Log{64}/Log{3}

N >= 1.806/0.477

N >= 3.785

As we can only consider whole integers for N, the number of trits needed to store a 6 bit number must be at least N = 4

In order to store n bits we can develop a similar expression to one noting that the number n of binary bits can store 2n decimal numbers

Thus we say that 3^N >= 2^n (2)

Again taking Logs to base 10 of both sides of (2) we get

N*Log{3} >= n*Log{2}

Thus the number of trits (N) necessary to fully express an n bit number is given by (3)

N >= n*Log{2}/Log{3} (3) {where N is the rounded up to the next whole integer}

(2)

Compute the data rate of the human ear from the following information. People can hear ...

#### Solution Summary

A number of questions are presented about data, data rates and data storage and compression and work examples to those question are presented. 5 such questions are presented and solutions provided