Introduction to the Base 26 Alphabet Numbers

=== by Bob Sutherland ===

If you use all of the letters of the alphabet as your digits you can create an alphabet number system.

Many computer spreadsheet programs use the alphabet number system to label the columns across the top of the screen while the rows going down the side of the screen are labelled with our normal base 10 decimal numbers.

There are 26 letters in the alphabet which become 26 digits when used as a number system.

The alphabet number system has a base (radix) of 26. Therefore the place value of each row is a power (exponent) of 26.

There is no number zero in the alphabet number system.

Your high school English teacher will teach you that a synonym is two words that mean the same thing. In high school Mathematics and Computer Science classrooms power and exponent are synonyms. Base and radix are synonyms when talking about number systems.

Here are the place values for the columns used by the alphabet number system:

Twenty-six to the power of five Twenty-six to the power of four Twenty-six cubed Twenty-six squared Twenty-sixes Ones
265 264 263 262 261 260
11881376 456976 17576 676 26 1

Notice how quickly the place values of the columns increase from right to left. That means that we could represent very large numbers with only a few alphabet digits by using this base 26 alphabet number system.

As a teacher I have often taught the alphabet number system at the same time that I was teaching the binary, octal, hexadecimal and decimal numbering systems. Some students found it helpful to scroll down a long list of Alphabet Numbers (base 26) to identify the patterns for themselves.