How to use the BIN2DEC function

What is the BIN2DEC function?

The BIN2DEC function converts a binary number to decimal.

1. Introduction

What is a binary number?

The binary system is a positional numeral system that uses only two digits: 0 and 1. The binary system is important in our society, many devices like computers, digital cameras, mobile phones and modern cars use binary code to store, process and communicate data. The binary numeral system makes it easy to store and transmit data using binary digits or bits.

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011

What is a decimal number?

The decimal system is a positional numeral system that uses 10 as the base, it requires 10 different numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The dot or the decimal point represents decimal fractions which are not whole numbers.

The decimal number 520 has three positions, each with a different weight. It starts with 10^0 on the right and increases by one power on each additional position to the left.

520 = (5*10^2)+(2*10^1)+(0*10^0)

520 = 500 + 20 + 0

2. Syntax

BIN2DEC(number)

number

Required. The binary number you want to convert. The sign bit is the most significant bit of number, the following 9 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

What is a sign bit?

The sign bit indicates whether a binary number is positive or negative, if the bit is 0 the number is positive, if the bit is 1, the number is negative.

What is a magnitude bit?

The remaining 9 bits are magnitude bits which represents the absolute value of the number. An absolute number is a number without the sign.

What is two's-complement notation?

Two’s-complement notation is when the magnitude bits are changed from 0 to 1 and 1 to 0 and adding 1 to the result, negative numbers are represented using two’s-complement notation. For example:

Decimal number +9 using 10 bits is 0000001001.
Decimal number -9 using 10 bits is 111110110 + 1 = 111110111

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3. Example 1

The image above demonstrates the BIN2DEC function cell C3, C4, C5, and C6. It calculates the decimal values based on the corresponding cells which contain different binary numbers.

Formula in cell C3:

The first cell B3 contains 11001 and the BIN2DEC function returns 25 in cell C3, the second cell B4 contains 11 and the BIN2DEC function returns 3.

The first cell B5 contains 100 and the BIN2DEC function returns 4 in cell C3, the second cell B6 contains 11111111 and the BIN2DEC function returns 255.

The next section describes how these values are calculated in detail.

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4. How is the function calculated in detail?

The binary system is also called the base-2 system because each digit represents a power of 2. The reason each digit represents a power of 2 is the position in a binary number has a weight that is a power of 2 starting from 2^0 on the right and increasing by one power on each additional position to the left.

Example 1

For example, the binary number 11001 has five positions, each with a different weight:

11001  = (1*2^4)+(1*2^3)+(0*2^2)+(0*2^1)+(1*2^0)

16+8+1 = 25

Example 2

11 = (1*2^1)+(1*2^0)

2+1 = 3

Example 3

100 = (1*2^2)+(0*2^1)+(0*2^0)

4+0+0 = 4

Example 4

11111111 = (1*2^7)+(1*2^6)+(1*2^5)+(1*2^4)+(1*2^3)+(1*2^2)+(1*2^1)+(1*2^0)

128+64+32+16+8+4+2+1 = 255

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5. Function not working

Maximum binary digits are 10 characters, in other words, the argument cannot contain more than 10 digits (10 bits). The BIN2DEC function will return a #NUM! error if this limit is exceeded.

5.1 Troubleshooting the error value

When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. The sixth line opens the Excel settings so you can adjust the Error Checking Options.

Here are a few of the most common Excel errors you may encounter.

#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.

#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.

#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.

#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.

#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.

#NAME error - The #NAME error happens if you misspelled a function or a named range.

#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.

#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.

#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.

5.2 The formula returns an unexpected value

To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that Here is how to troubleshoot a formula:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
   The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. Repeat press with left mouse button oning the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
6. Press "Close" button to dismiss the dialog box.

There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a hunch that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.

The image above shows cell reference B3 converted to hard-coded value using the F9 key. The hardcoded value is a text string and the EOMONTH function expects a number representing the Excel date. We have found what is wrong with the formula using the F9 key.

Tips!

• View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
• Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
• Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.

Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button

Other errors

Floating-point arithmetic may give inaccurate results in Excel - Article

Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.

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6. How to convert binary 8 bit to the ANSI character set

The ANSI system is an extended version of the ASCII system often used in Microsoft windows, it adds another 128 characters. ASCII assigns standard numeric values to letters, numbers, and other characters used in computers. For example, the letter A has the value 65, the digit 0 has the value 48, and the period (.) has the value 46.

ASCII uses seven-bit binary numbers to represent these values. Since there are 128 different possible combinations of seven 0s and 1s, the code can represent 128 different characters. The ANSI encoding adds another 128 characters, see the image above. For example, the letter A is represented by the binary number 01000001, and the digit 0 is represented by the binary number 00110000.

This formula converts a single 8 bit binary number to its equivalent character in the ANSI system.

Formula in cell C3:

Explaining formula

Step 1 - Convert binary to decimal

The BIN2DEC function converts a binary number to the decimal number system.

Function syntax: BIN2DEC(number)

BIN2DEC(B3)

becomes

BIN2DEC("01000001")

and returns 65.

Step 2 - Convert decimal to ANSI character

The CHAR function converts a number to the corresponding ANSI character determined by your computers character set.

Function syntax: CHAR(text)

CHAR(BIN2DEC(B3))

becomes

CHAR(65)

and returns

"A".

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7. Convert multiple binary digit groups

This example demonstrates how to convert multiple 8 bit binary strings to characters, the binary strings are separated by a blank (space).

Formula in cell C3:

For example, 01001000 has 8 bits. The corresponding decimal number is 72 which is character "H" in the ANSI system.

Explaining formula

Step 1 - Split string based on a delimiter

The TEXTSPLIT function splits a string into an array based on delimiting values.

Function syntax: TEXTSPLIT(Input_Text, col_delimiter, [row_delimiter], [Ignore_Empty])

TEXTSPLIT(B3," ")

becomes

TEXTSPLIT("01001000 01100101 01101100 01101100 01101111"," ")

and returns

{"01001000", "01100101", "01101100", "01101100", "01101111"}.

Step 2 - Convert binary to decimal

The BIN2DEC function converts a binary number to the decimal number system.

Function syntax: BIN2DEC(number)

BIN2DEC(TEXTSPLIT(B3," "))

becomes

BIN2DEC({"01001000", "01100101", "01101100", "01101100", "01101111"})

and returns

{72,101,108,108,111}

Step 3 - Convert decimal to ANSI character

The CHAR function converts a number to the corresponding ANSI character determined by your computers character set.

Function syntax: CHAR(text)

CHAR(BIN2DEC(TEXTSPLIT(B3," ")))

becomes

CHAR({72,101,108,108,111})

and returns

{"H","e","l","l","o"}

Step 4 - Join characters

The TEXTJOIN function combines text strings from multiple cell ranges.

Function syntax: TEXTJOIN(delimiter, ignore_empty, text1, [text2], ...)

TEXTJOIN("",1,CHAR(BIN2DEC(TEXTSPLIT(B3," "))))

becomes

TEXTJOIN,"",1,{"H","e","l","l","o"})

and returns

"Hello".

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Useful links

BIN2DEC Function - Microsoft
Binary to Decimal converter
How to Convert from Binary to Decimal

'' function examples

Functions in 'Engineering' category

The BIN2DEC function function is one of 42 functions in the 'Engineering' category.

Excel function categories

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