The BIN2DEC function converts a binary number to decimal.

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

1. BIN2DEC Function Syntax

BIN2DEC(number)

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2. BIN2DEC Function Arguments

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. BIN2DEC Function example

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 B3:

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 BIN2DEC 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. BIN2DEC 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.

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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

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The following article has a formula that contains the function.

Functions in 'Engineering' category

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

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