Question

Determine the amount of information in a message of sources with the following

possible messages:
a) capital and small letters of the Latin alphabet;
b) capital and small letters of the Greek alphabet;
c) capital and small letters of the Romanian alphabet;
d) decimal digits 0, 1, 2, ..., 9;
e) the numbers 0, 1, 2, ..., 9, the signs +, –, ×, / and brackets ( );
f) numerical indications of the form hh:mm (hh – hour, mm – minutes) of a clock
electronic;
g) numerical indications of the form hh:mm:ss (ss – seconds) of an electronic clock;
h) numerical indications of the form zz.ll.yy (dd – day, ll – month, yy – year) of a
electronic calendar

Answer 1

To determine the amount of information in a message, it is important to calculate the number of unique symbols that could be used for each specific set of characters or symbols. Different alphabets and numeric systems have varying amounts of unique symbols, influencing the amount of information content. For time and date representations, the total possible combinations are calculated based on conventional representations of hours, minutes, seconds, and dates.

Step-by-step explanation:

To determine the amount of information in a message, we need to calculate the number of possible messages that can be represented by a source. The amount of information depends on the number of unique symbols or elements that can be used in the message.

• Capital and small letters of the Latin alphabet: There are 26 capital letters and 26 small letters, totaling 52 unique symbols.
• Capital and small letters of the Greek alphabet: The Greek alphabet has 24 letters and considering both capital and small forms, there are 48 unique symbols.
• Capital and small letters of the Romanian alphabet: The Romanian alphabet has 31 letters and with both capital and small forms, there are 62 unique symbols.
• Decimal digits: There are 10 digits (0-9), so there are 10 unique symbols.
• The numbers 0-9, the signs +, –, ×, /, and brackets ( ): This set includes 15 unique symbols (10 digits and 5 signs/brackets).
• Numerical indications of the form hh:mm of an electronic clock: Since there are 24 hours and 60 minutes, the total number of combinations is 24 times 60, which equals 1,440 unique messages.
• Numerical indications of the form hh:mm:ss of an electronic clock: There are 24 hours, 60 minutes, and 60 seconds, yielding 86,400 unique messages (24*60*60).
• Numerical indications of the form zz.ll.yy of an electronic calendar: Assuming valid dates only, this will vary depending on the range of years and months allowed, and the number of days in each month.

To calculate the information content formally, one would use the base-2 logarithm of the number of unique symbols/messages, measured in bits.