# BASE

In this comprehensive guide, we will explore the Excel formula “BASE,” which is used to convert a number from a decimal (base 10) to another base (between 2 and 36). This function is particularly useful when working with different numeral systems, such as binary, octal, or hexadecimal. We will cover the syntax, examples, tips and tricks, common mistakes, troubleshooting, and related formulae for the BASE function.

## BASE Syntax

The syntax for the BASE function in Excel is as follows:

Where:

• number (required) is the decimal number you want to convert to another base.
• radix (required) is the base to which you want to convert the number. It must be an integer between 2 and 36.
• min_length (optional) is the minimum length of the result. If the result has fewer digits than specified, it will be padded with zeros. If omitted, the default value is 1.

## BASE Examples

Let’s look at some examples of using the BASE function in Excel:

1. Converting a decimal number to binary: To convert the decimal number 10 to binary (base 2), you would use the formula =BASE(10, 2). The result would be “1010”.
2. Converting a decimal number to octal: To convert the decimal number 100 to octal (base 8), you would use the formula =BASE(100, 8). The result would be “144”.
3. Converting a decimal number to hexadecimal: To convert the decimal number 255 to hexadecimal (base 16), you would use the formula =BASE(255, 16). The result would be “FF”.
4. Using the min_length argument: To convert the decimal number 5 to binary with a minimum length of 4 digits, you would use the formula =BASE(5, 2, 4). The result would be “0101”.

## BASE Tips & Tricks

Here are some tips and tricks to help you get the most out of the BASE function in Excel:

• Remember that the radix must be between 2 and 36. If you need to work with a base outside of this range, you will need to use a custom formula or a different method.
• When converting to bases larger than 10, the result will include letters (A-Z) to represent values 10-35. For example, when converting to base 16 (hexadecimal), the letters A-F represent the values 10-15.
• If you need to convert a number from one non-decimal base to another, you can use the BASE function in combination with the DECIMAL function. First, convert the number to decimal using the DECIMAL function, and then convert the result to the desired base using the BASE function.

## Common Mistakes When Using BASE

Here are some common mistakes to avoid when using the BASE function in Excel:

• Using a radix outside the allowed range (2-36) will result in a #NUM! error. Make sure your radix is within the valid range.
• Using a negative number or a non-integer value for the radix or min_length arguments will result in a #VALUE! error. Ensure that these arguments are positive integers.
• Forgetting to include the min_length argument when you need a specific number of digits in the result. If you need a fixed-length result, make sure to include the min_length argument in your formula.

## Why Isn’t My BASE Function Working?

If you’re having trouble with the BASE function, consider the following troubleshooting steps:

1. Double-check your formula syntax, ensuring that you have the correct number of arguments and that they are in the correct order.
2. Make sure your radix is within the allowed range (2-36) and that it is a positive integer.
3. Ensure that the min_length argument, if used, is a positive integer.
4. Check for any errors in your input data, such as non-numeric values or incorrect cell references.

## BASE: Related Formulae

Here are some related Excel formulae that you may find useful when working with the BASE function:

1. DECIMAL: This function converts a number from a specified base to decimal (base 10). The syntax is DECIMAL(text, radix).
2. HEX2DEC: This function converts a hexadecimal number to decimal. The syntax is HEX2DEC(number).
3. HEX2BIN: This function converts a hexadecimal number to binary. The syntax is HEX2BIN(number, [places]).
4. HEX2OCT: This function converts a hexadecimal number to octal. The syntax is HEX2OCT(number, [places]).
5. BIN2DEC: This function converts a binary number to decimal. The syntax is BIN2DEC(number).

By mastering the BASE function and its related formulae, you can efficiently work with numbers in different numeral systems and perform various conversions in Excel.

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