# A to Z of Excel Functions: the BIN2DEC Function

19 December 2016

*Welcome back to our regular A to Z of Excel Functions blog. Today we look at the BIN2DEC function. *

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**The BIN2DEC function**

This function converts a binary number (base two) to a decimal number (base 10).

The **BIN2DEC **function employs the following syntax to operate:

**BIN2DEC(number)**

The **BIN2DEC** function has the following arguments:

**number:**this is required and represents the binary number you wish to convert to a decimal**number**cannot contain more than 10 characters (10 bits)- the most significant bit of
**number**is the sign bit - the remaining nine bits are magnitude bits
- negative numbers are represented using
**two's-complement**notation.

**Two's complement** is a mathematical operation on binary numbers, as well as a binary signed number representation based on this operation. The two's complement of an **N**-bit number is defined as the complement with respect to 2** ^{N}**; in other words, it is the result of subtracting the number from 2

**. This is also equivalent to taking the ones' complement and then adding one, since the sum of a number and its ones' complement is all 1 bits. The two's complement of a number behaves like the negative of the original number in most arithmetic, and positive and negative numbers can coexist in a natural way.**

^{N}In English then, if number is 10 digits and the first number is 1, the number is deemed negative and 2^{9} (512) is subtracted from it, *e.g.* **BIN2DEC(1111111111)** = -1, being 511 (111111111 as a decimal) less 512.

It should be further noted that if **number** is not a valid binary number, or if number contains more than 10 characters (10 bits), **BIN2DEC** returns the *#NUM!* error value.

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.*