Assume a ternary computer in which the basic unit of memory is a “trit” (ternary

Question

Assume a ternary computer in which the basic unit of memory is a “trit” (ternary digit) rather than a bit. A trit can have three possible settings (0, 1 and 2) rather than just two (0 and 1). Show how nonnegative integer can be represented in ternary notation using trits by a method analogous to binary notation using bits. Is there any nonnegative integer that can be represented using ternary notation and trits that cannot be represented using binary notation and bits? Are there any that can be represented using bits that can not be represented using trits? Why are binary computers more common than ternary computers?

Explanation / Answer

A ternary number system has base 3,the basic unit of memory in ternary number system is tits.

one trit = log23(1.58496) bits

Given is representation of 10 decimal numbers in bits and tits

For example take 365

365 in binary 101101101 and in ternary 111112

Ternary number system can be used to represent all non negative integers, there is no non negative integer that can be represented in tits but not in bits or vice versa

Binary computers are common because it is easy to set the logic gates or the transistors in two states i.e. one and off ( 1 or 0) but it is very difficult to set the electronic devices in three states since ternary computers will use more than two states.

TERNARY 1 2 10 11 12 20 21 22 100 BINARY 1 10 11 100 101 110 111 1000 1001 DECIMAL 1 2 3 4 5 6 7 8 9

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