In international Morse code, each letter in the alphabet is symbolized by a series of dots...

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 “×- ” while the most common letter “e” has the shortest code “×” (just a dot). What is the minimum number of dots and/or dashes needed to represent any letter in the English alphabet (26 letters)?

Solutions

Expert Solution

There are 26 letters in the alphabet, so we need a code that handle at least that many characters.

1 position and one can decide to use one of two symbols each, that gives 2¹=2 words
2 positions and one can decide to use one of two symbols each, that gives 2²=4 words
3 positions and one can decide to use one of two symbols each, that gives 2³=8 words
4 positions and one can decide to use one of two symbols each, that gives 2⁴=16 words

Total combination of dots and dashes = 2 + 4 + 8 + 16 = 30

Therefore, the answer is 4 i.e, the minimum number of dots and/or dashes needed to represent any letter in the English alphabet (26 letters is 4.

Here is repesentaion of each alphabet in morse code:

A= .-
B= -...
C= -.-.
D= -..
E= .
F= ..-.
G= --.
H= ....
I= ..
J= .---
K= -.-
L= .-..
M= --
N= -.
O= ---
P= .--.
Q = --.-
R= .-.
S= ...
T= -
U= ..-
V= ...-
W =.--
X =-..-
Y= -.--
Z= --..

Note: I hope this would help, but if you still have any doubt please let me know.

milcah answered 3 weeks ago

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