# BASE Function

Converts a number into the supplied base

Converts a number into the supplied base

The BASE function is available under Mathematical and Trigonometric functions. The function returns a text representation of the calculated value and will convert a number into the supplied base (radix). BASE was introduced in Excel 2013 and is unavailable in earlier versions.

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

The BASE function uses the following arguments:

**Number**(required argument) – It is the number that we wish to convert. The number should be an integer and greater than or equal to 0 and less than 2^53.**Radix**(required argument) – The base radix is what we want to convert the number into. It must be an integer greater than or equal to 2 and less than or equal to 36. Radix is the number of unique digits, including zero, used to represent numbers in a positional numeral system. For example, for the decimal system, the radix is 10, as it uses ten digits from 0 to 9.**Min_length**(optional argument) – It is the minimum length of the string returned. If specified, it must be an integer greater than or equal to 0.

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To understand the uses of the BASE function, let’s consider a few examples:

Suppose we want to convert the number 10 to base 2:

The BASE function will convert the decimal number 10 to base 2 (binary system) and give us the following result:

On a similar basis, we can give different radix to get the desired output. Few examples are shown below:

Now, let’s see how this function behaves when we specify a minimum_length argument. Suppose we specify the number 12, with radix 2 and minimum length 10:

In the example, the function will convert the decimal number 12 to base 2 (binary), with a minimum length of 10. The result would be 0000001100, which is 1100 with 6 leading zeros to make the string 10 characters long.

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- #VALUE! error – Occurs when the number given is a non-numeric value.
- #NUM! error – When any of the argument that is number, radix, or min_length is outside the minimum or maximum constraints. So, the error will occur:
- When the given number argument is < 0 or is ≥ 2^53.
- When the given radix argument is < 2 or > 36.
- When the [min_length] argument is supplied and is < 0 or ≥ 256.

- #NAME! error – Occurs when the formula contains an unrecognized value in any of the arguments.
- If we enter a non-integer number, the argument is truncated to an integer.
- The maximum value of the min_length argument is 255.
- If we enter the min_length argument, leading zeros are added to the result if the result would otherwise be shorter than the minimum length specified. For example, BASE(32,2) returns 100000, but BASE(32,2,8) returns 00100000.
- The function can also be used by specifying a cell reference. If the cell referred to is empty, it will take the number as zero.

For example, if we give the formula =BASE(A3,2,10), wherein A3 is the cell referred to and is empty. In such scenario, the BASE function will return the following result as A3 is empty.

**Click here to download the sample Excel file**

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