Question

In international morse code, each letter in the alphabet is symbolized by a series of dots and dashes: the letter a, for example, is encoded as "· –". what is the min- imum number of dots and/or dashes needed to represent any letter in the english alphabet?

Answer 1

Morse code is essentially the same as binary. That is, there are two "digits", a dot or a dash.

There are 26 letters in the English alphabet. Clearly, we can't just use one dot or dash, since that could only encode 2 letters at the most. We can't use two symbols because that could only encode 4 letters at the most. Similarly, 3 symbols means $2^3=8$ letters at most.

We have to select the smallest power of 2 that exceeds or is equal to 26. In this case, $2^5=32>26$, so we would have to use up to 5 symbols to encode each letter in the alphabet.