A binary code is a system of binary numbers with a fixed number of digits that are used to represent letters, numbers, and symbols. To produce enough binary numbers to represent all of the letters of our alphabet, how many binary digits must be used?

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Answer 1 · 2017-04-18T05:16:51

At least #5# binary digits are required

The number of possibilities for only one binary digit is #2#: #0# or #1#.

The number of possibilities for two binary digits is #4#: #00#, #01#, #10#, or #11#.

The number of possibilities for three binary digits is #8#: #000#, #001#, #010#, #011#, #100#, #101#, #110#, or #111#.

The number of possibilities for #n# binary digits is #2^n#.

There are #26# letters in the alphabet. Since #2^5=32>26#, at least #5# binary digits are required.