# DECIMAL

In this comprehensive guide, we will explore everything you need to know about the DECIMAL function in Excel. The DECIMAL function is a useful tool for converting text representations of numbers in a specific base (radix) into decimal numbers. This function is particularly helpful when working with different numeral systems, such as binary, octal, or hexadecimal.

## DECIMAL Syntax

The syntax for the DECIMAL function is as follows:

Where:

• text is the text representation of the number you want to convert to a decimal number. This can be a cell reference, a text string, or a number.
• radix is the base of the numeral system you are converting from. This can be any integer between 2 and 36, inclusive.

## DECIMAL Examples

Let’s look at some examples of how to use the DECIMAL function in Excel:

Example 1: Converting a binary number to decimal

Suppose you have a binary number “1011” and you want to convert it to a decimal number. You can use the DECIMAL function as follows:

=DECIMAL(“1011”, 2)

This formula will return the decimal number 11, as the binary number 1011 is equal to 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 11 in decimal.

Example 2: Converting a hexadecimal number to decimal

If you have a hexadecimal number “1A3” and you want to convert it to a decimal number, you can use the DECIMAL function like this:

=DECIMAL(“1A3”, 16)

This formula will return the decimal number 419, as the hexadecimal number 1A3 is equal to 1 * 16^2 + 10 * 16^1 + 3 * 16^0 = 419 in decimal.

Example 3: Converting an octal number to decimal

For an octal number “725”, you can convert it to a decimal number using the DECIMAL function as follows:

=DECIMAL(“725”, 8)

This formula will return the decimal number 469, as the octal number 725 is equal to 7 * 8^2 + 2 * 8^1 + 5 * 8^0 = 469 in decimal.

## DECIMAL Tips & Tricks

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

1. Remember that the radix must be an integer between 2 and 36. If you enter a value outside of this range, Excel will return a #NUM! error.
2. If the text argument contains characters that are not valid for the specified radix, Excel will return a #VALUE! error. For example, if you try to convert the text “1A3” with a radix of 8, you will get a #VALUE! error because the characters “A” and “B” are not valid in the octal numeral system.
3. When converting from a numeral system with a base greater than 10, use uppercase letters (A-Z) to represent the additional digits. For example, in the hexadecimal system, the digits 10-15 are represented by the letters A-F.
4. You can use the DECIMAL function in combination with other functions to perform more complex calculations. For example, you can use the DECIMAL function to convert a binary number to decimal, and then use the SUM function to add it to another decimal number.

## Common Mistakes When Using DECIMAL

Here are some common mistakes to avoid when using the DECIMAL function:

1. Using an invalid radix: Make sure the radix is an integer between 2 and 36. If you enter a value outside of this range, Excel will return a #NUM! error.
2. Using invalid characters for the specified radix: Ensure that the text argument contains only valid characters for the specified radix. If it contains invalid characters, Excel will return a #VALUE! error.
3. Forgetting to use uppercase letters for numeral systems with a base greater than 10: When converting from a numeral system with a base greater than 10, use uppercase letters (A-Z) to represent the additional digits.

## Why Isn’t My DECIMAL Function Working?

If your DECIMAL function is not working as expected, check for the following issues:

1. Ensure that the radix is an integer between 2 and 36. If you enter a value outside of this range, Excel will return a #NUM! error.
2. Check that the text argument contains only valid characters for the specified radix. If it contains invalid characters, Excel will return a #VALUE! error.
3. Make sure you are using uppercase letters for numeral systems with a base greater than 10. If you use lowercase letters, Excel may return a #VALUE! error.

## DECIMAL: Related Formulae

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

1. BASE: The BASE function is the inverse of the DECIMAL function. It converts a decimal number to a text representation in a specified base (radix). The syntax for the BASE function is: =BASE(number, radix, [min_length]).
2. HEX2DEC: The HEX2DEC function converts a hexadecimal number to a decimal number. The syntax for the HEX2DEC function is: =HEX2DEC(number).
3. DEC2HEX: The DEC2HEX function converts a decimal number to a hexadecimal number. The syntax for the DEC2HEX function is: =DEC2HEX(number, [places]).
4. HEX2BIN: The HEX2BIN function converts a hexadecimal number to a binary number. The syntax for the HEX2BIN function is: =HEX2BIN(number, [places]).
5. DEC2BIN: The DEC2BIN function converts a decimal number to a binary number. The syntax for the DEC2BIN function is: =DEC2BIN(number, [places]).

By mastering the DECIMAL function and its related formulae, you can easily work with different numeral systems in Excel and perform a wide range of calculations and conversions.

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