Morse code isn't binary, it's trinary.
You have 3 signals: dots, dashes, and spaces.
Here's the relevant extract from the wikipedia article on Morse Code:
> Each Morse code symbol is formed by a sequence of dots and dashes. The dot duration is the basic unit of time measurement in Morse code transmission. The duration of a dash is three times the duration of a dot. Each dot or dash within a character is followed by period of signal absence, called a space, equal to the dot duration. The letters of a word are separated by a space of duration equal to three dots, and the words are separated by a space equal to seven dots