# BASE Function in Excel – Change the Radix

BASE Function in Excel is a very interesting type of Mathematical Function. We use the Decimal Number System to represent numbers using the digits from 0 to 9. The base of the Decimal Number system is 10. This logic would help you better understand the BASE Function.

So here we go.

## When to Use the BASE Function in Excel?

If BASE Function could be defined in a single line, then BASE Function converts a numerical value into its value in a specified base ( radix ). The BASE Function returns the text representation of any number converted to a particular base.

The numbers we use in real life have a base of 10 because we represented them using the digits from 0 to 9 ( 10 digits ).

## What is the Base of theNumber System?

Base refers to the number of digits that we can use to represent a number. For instance, when we say that we can use the digits from 0 to 9 to write any number, we mean that those numbers would have a base of 10 ( total digits from 0 to 9 ).

We can understand this with one more example. If we want to write a number using only 4 digits ( 0 to 3 ) then the base of the number would be 4. In this case, we can only use a combination of digits from 0 to 3 to represent any number. i.e (321)4, (203)4

A computer only understands Binary language. With Binary, we mean the base of all the numbers would be 2 and we can use only 2 digits ( 0 and 1 ) to represent any number. i.e. (1011)2, (1100)2

Now, the BASE Function converts a numerical value ( having base 10 ) into the specified base value.

## Syntax and Arguments

The following points contain information regarding the BASE Function of Excel.

• number – This is the numerical value whose radix we want to change. Its value lies between 0 and 253
• radix – This is the new base for our numerical value. radix must be an integer such that it lies between 2 and 36 ( including 2 and 36 ). If the base is n, then the result of the BASE function would be a combination of digits from 0 to (n-1) digits.
• [min_length] – This is the minimum length of our result. If the length of result is smaller than min_length then the result is left padded with zeroes. It is an optional argument.

## Examples to Learn the Base Function in Excel

In this section of the blog, we would execute some examples to implement the BASE Function in Excel.

### Example 1 – Simplest Example to Learn BASE Function

Let us suppose we want to change the base of 1924 ( base 10 ) to base 4. We can use the BASE Function Formula to get results.

Use the following BASE Formula.

`=BASE(1924,4)`

As a result, the formula has returned 132010.

Explanation – We have supplied the number and radix argument of the BASE Function as 1924 and 4 respectively. So the number 1924 is converted to base 4. The result is 132010 ( use of digits from 0 to 4 only ).

### Example 2 – Decimal to Binary Number Conversion

The Base of the Binary number system is 2 which means that it uses only 2 digits 0 and 1 to represent all digits that can be represented using the decimal number system.

Let us suppose we have the following numerical values ( default base is 10 ) in the range A2:A10.

Use the following formula in cell B2 to get the numbers converted into Binary Number System.

`=BASE(A2,2)`

Select the range B2:B10 and press the Ctrl D key.

As a result, the formula converts the numbers into binary values.

Explanation – We have supplied cell A2 ( containing 24 ) as the BASE Function number argument. The radix is supplied as 2. As a result, the formula returned the base 2 value of 23 as 11000.

### Example 3 – Base Greater than 10

Let us suppose we want to convert 324 into base 12.

Use the following BASE Formula.

`=BASE(3241,12)`

As a result, the formula returns 1A61.

Explanation – For a Base greater than 10, the use of characters in the representation of numbers is totally valid, For Base 12 we can use a total of 12 characters:-

• Digits from 0 to 9 ( 10 ) and
• Alphabets A and B ( 2 )

Where 0 to 9 are the numbers and A represents 10, B represents 11.

## Left Padding the Result with Zeroes

Let us say we need to convert 12 into a binary number system. Use the following formula,

The formula returns 1100. We want this result to have 6 digits in total. So, update the formula to:-

`=BASE(12,2,6)`

Since the result was 1100, the formula has left padded the two empty spaces with zeroes to make the result of length 6.

Explanation – We have supplied the min_length optional argument as 6.

## Important Notes for BASE Function

This is the very essential information for the BASE Function defined below.

• The BASE Function results in a #NUM! error for non-numerical arguments.
• If the number argument is not an integer, then the digits after decimal would be truncated.
• The number, radix and num_length argument must lie under specified values.

This brings us to the end of the blog.

Thank you for coming.