Morse code is used to send messages. Each symbol is represented by a series of dots and dashes. Why is it sufficient to use at most five dots and/or dashes to represent any symbol?

1 Answer
MathFact-orials.blogspot.com
Feb 14, 2017

#2^5# "bits" translates to 32 characters, while the English alphabet has 26 letters

Explanation:

Let's approach this question this way - how many characters might someone want to send using Morse Code? There are 26 letters in the alphabet, so we need a code that handle at least that many characters.

Each character is represented by a series of dots and/or dashes - with each dot/dash being effectively a choice between 2 different bits (a dot and a dash being a "bit").

If we had one bit represent a character, we could make 2 characters.

If we had two bits represent a character, we could make #2xx2=2^2=4# characters.

If we had three bits, that'd be #2^3=8# characters

Four bits gets us #2^4=16#

And five bits gets us #2^5=32# characters.

Related questions
See all questions in Combinations and Permutations
Impact of this question
5043 views around the world
You can reuse this answer
Creative Commons License