# A to Z of Excel Functions: the BASE Function

21 October 2016

*Welcome back to our regular A to Z of Excel Functions blog. Today we look at the BASE function. *

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**The BASE function**

This function converts a **number** into a text representation with the given radix (base). Clear as mud if you speak gobbledygook.

What does it mean in English? **BASE **converts a **number **in decimal (base 10) to a different base (which is known as the **radix**). Let me provide an example. Take the number 37. In base 3, this can be represented as:

(1 x 3^{3}) + (**1** x 3^{2}) + (**0** x 3^{1}) + (**1** x 3^{0})

= (1 x 27) + (**1** x 9) +(**0** x 3) + (**1** x 1)

= 27 + 9 + 0 + 1

So in base 3 this is the text representation 1101. If we needed this representation to be of minimum length (**min_length**) 8, then

27 = (0 x 3^{7}) + (**0** x 3^{6}) + (**0** x 3^{5}) + (**0** x 3^{4}) + (**1** x 3^{3}) + (**1** x 3^{2}) + (**0** x 3^{1}) + (**1** x 3^{0})

=00001101.

Makes sense now?

The **BASE** function has only been around since Excel 2013 so it will not work in earlier versions of Excel. It employs the following syntax to operate:

**BASE(number, radix, [min_length])**

The **BASE** function has the following arguments:

**number:**this is required and represents the number that you want to convert. This must be an integer greater than or equal to 0 and less than 2^{53}**radix:**this is also required and represents the base radix that you want to convert the number into. This must be an integer greater than or equal to 2 and less than or equal to 36*(why 36??)***min_length:**this is optional. This represents minimum length of the returned string and must be an integer greater than or equal to zero if specified.

It should be further noted that:

- If
**number**,**radix**, or**min_length**are outside the minimum or maximum constraints,**BASE**returns the*#NUM!*error value - If
**number**is a non-numeric value,**BASE**returns the*#VALUE!*error value - Any non-integer number entered as an argument is truncated to an integer
- If the
**min_length**argument is included, leading zeros are added to the result if the result would otherwise be shorter than the minimum length specified. For example,**BASE(16,2)**returns 10000, but**BASE(16,2,8)**returns 00010000 - The maximum value of the
**min_length**argument is 255.

Please see my example below:

*We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every other business day.*