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C# floating point to binary string and vice versa

I am converting a floating point value to binary string representation:
float resulta = 31.0 / 15.0; //2.0666666
var rawbitsa = ToBinaryString(resulta); //returns 01000000000001000100010001000100
where ToBinaryString is coded as:
static string ToBinaryString(float value)
{
int bitCount = sizeof(float) * 8; // never rely on your knowledge of the size
// better not use string, to avoid ineffective string concatenation repeated in a loop
char[] result = new char[bitCount];
// now, most important thing: (int)value would be "semantic" cast of the same
// mathematical value (with possible rounding), something we don't want; so:
int intValue = System.BitConverter.ToInt32(BitConverter.GetBytes(value), 0);
for (int bit = 0; bit < bitCount; ++bit)
{
int maskedValue = intValue & (1 << bit); // this is how shift and mask is done.
if (maskedValue > 0)
maskedValue = 1;
// at this point, masked value is either int 0 or 1
result[bitCount - bit - 1] = maskedValue.ToString()[0];
}
return new string(result); // string from character array
}
Now I want to convert this binary string to float value.
I tried the following but it returns value "2.8293250329111622E-315"
string bstra = "01000000000001000100010001000100";
long w = 0;
for (int i = bstra.Length - 1; i >= 0; i--) w = (w << 1) + (bstra[i] - '0');
double da = BitConverter.ToDouble(BitConverter.GetBytes(w), 0); //returns 2.8293250329111622E-315
I want the value "2.0666666" by passing in value "01000000000001000100010001000100"
Why am I getting a wrong value? Am I missing something?

You're making this a lot harder than it needs to be; the error seems to be mostly in the character parsing code, but you don't need to do all that.
You could try like this instead:
static string ToBinaryString(float value)
{
const int bitCount = sizeof(float) * 8;
int intValue = System.BitConverter.ToInt32(BitConverter.GetBytes(value), 0);
return Convert.ToString(intValue, 2).PadLeft(bitCount, '0');
}
static float FromBinaryString(string bstra)
{
int intValue = Convert.ToInt32(bstra, 2);
return BitConverter.ToSingle(BitConverter.GetBytes(intValue), 0);
}
Example:
float resulta = 31.0F / 15.0F; //2.0666666
var rawbitsa = ToBinaryString(resulta);
Console.WriteLine(rawbitsa); //01000000000001000100010001000100
var back = FromBinaryString(rawbitsa);
Console.WriteLine(back); //2.0666666
Note that the usage of GetBytes is kinda inefficient; if you're OK with unsafe code, you can remove all of that.
Also note that this code is CPU-specific - it depends on the endianness.

Converting fractions to binary string?

To convert an integer value, manually, to binary string you (one technique is to) continuously divide by 2 till the quotient > 0 and append the remainder in reverse order.
string decimalToBinary(int n)
{
string binary = string.Empty;
while (n > 0)
{
// get the LSB
int remainder = n % 2;
// truncate the LSB
n /= 2;
// insert remainder in front
binary = remainder.ToString() + binary;
}
return binary;
}
However, I can't figure out how to convert a fraction (floating point number like for example -0.30), to binary string. More specifically what algorithm should I use. Could anyone suggest an idea?

To convert an integer value, manually
Note that since your input is a an integer which can be negative or zero. But your condition for the while loop is while (n > 0)
Therefore, your code right now cannot handle the situation when the input is 0 (it will return string.Empty) or negative (it will return nothing).
To fix it, you may consider to change your input to uint and make special case for n == 0:
string decimalToBinary(uint n) //note this uint
{
if (n == 0) //special case
return "0";
string binary = string.Empty;
while (n > 0)
{
// get the LSB
uint remainder = n % 2;
// truncate the LSB
n /= 2;
// insert remainder in front
binary = remainder.ToString() + binary;
}
return binary;
}
Or you change it internally:
private string decimalToBinary(int n) {
string binary = string.Empty;
if (n == 0)
return "0";
uint p = (uint)n; //note this cast
while (p > 0) {
// get the LSB
uint remainder = p % 2;
// truncate the LSB
p /= 2;
// insert remainder in front
binary = remainder.ToString() + binary;
}
return binary;
}
Then you should get what you want.

Here is a C++ implementation for fraction to binary conversion:
double frac = .1;
int digits = 1, intpart;
cout <<".";
while (digits < 32 && frac != 0.)
{
frac = frac * 2;
intpart = frac;
frac = frac - intpart;
cout << intpart;
digits++;
}
Output: .0001100110011001100110011001100
or using recursion:
#include <iostream>
using namespace std;
void fractobin(double frac, int digits);
//==========================================================
int main()
{
cout <<".";
fractobin(.1, 1);
return 0;
}
//==========================================================
void fractobin(double frac, int digits)
{
int intpart;
if (digits >=32 || frac==0.)
{
return;
}
else
{
frac = frac * 2;
intpart = frac;
cout << intpart;
fractobin(frac - intpart, ++digits);
return;
}
}

C# code issue for ASCII to HEX. insight required

I am doing me university project and facing a big issue. i am developing a UI on C# visual studio 2010. I need to open a serial connection and feed some values into the micro controller. basically i have nodes with 24 bits addresses (3 bytes) e.g 0x78A26F.
i take my input from user in the GUI in a text Box. the user shall enter this 78A26F and i want that the serial port sends the following data 0x6F 0xA2 0x78.
But the user input is saved as a string and when i send it through serial connection, the ASCII are sent e.g 0x37 0x38 0x41 0x32 0x36 0x46. i can do the processing in the uC and perform some checks to subtract 0x30 if between 0x30 and 0x39 or subtract 0x37 if between 0x41 and 0x46. but i do not want to use the uC for this calculations. i want to implement some algorithm in the GUI c# for sending the correct HEX value. So i wrote the following program. but i am getting an error. "Value was either too large or too small for an unsigned byte." at code line stating (data[2 - i] = Convert.ToByte(x*16 + y)).
I am unable to figure out this issue and fed up now as this should not happen in any case.
if anyone can help me in this regard, either with this code or any other algo/method, i will be really thankful. please, I would prefer never to implement some algo on uC.
Thanks
Maleeha
/***********************************************************************/
/*The code for opening the serial connection and converting it appropriately*/
/***********************************************************************/
byte[] conversion()
{
string text = label16.Text.ToUpper(); // if user enters not capital letters
byte[] data = new byte[3];
int x, y;
bool valid;
for (int i = 2; i >= 0; i--)
{
valid = true;
x = (Convert.ToInt32(Convert.ToChar(text[2 * i + 1])));
y = (Convert.ToInt32(Convert.ToChar(text[2 * i]))); // I want to first send the 0x6F then 0xA2 and finally 0x78. ToChar is so that i can check for A-F
if(x >= 48 || x <= 57) // i,e it is already a number
x = Convert.ToInt32(text[2 * i + 1]);
else if (x >= 65 || x <= 70) // it is between A-F
x = x - 55; // in case of A, i get 10
else // any other value i.e greater than F or any other.
{
valid = false;
break;
}
if (y >= 48 || y <= 57) // same for y
y = Convert.ToInt32(text[2 * i]);
else if (y >= 65 || y <= 70)
y = y - 55;
else
{
valid = false;
break;
}
if (valid == true)
data[2 - i] = Convert.ToByte(x*16 + y); // max will be 15*16 + 15 = 255 which should be OK for convert.ToByte.
}
return data;
}
void serial(byte[] text)
{
SerialPort serialPort1 = new SerialPort();
//configuring the serial port
serialPort1.PortName = "COM1";
serialPort1.BaudRate = 9600;
serialPort1.DataBits = 8;
serialPort1.Parity = Parity.None;
serialPort1.StopBits = StopBits.One;
//opening the serial port
serialPort1.Open();
//write data to serial port
serialPort1.Write(text, 0, 3);
//close the port
serialPort1.Close();
}
/***********************************************************************/
private void button3_Click(object sender, EventArgs e)
{
byte[] data = conversion();
serial(data);
}

The .NET framework already supports converting hex strings. Make your code look like this:
uint value;
if (!uint.TryParse(label16.Text, // Ought to be a text box
System.Globalization.NumberStyles.HexNumber, null, out value)) {
MessageBox.Show("Invalid hex value");
return;
}
serialPort1.Write(BitConverter.GetBytes(value), 0, 3);

Can you use the built in methods?
byte[] conversion()
{
string text = label16.Text;
for (int i = 0; i < text.length - 1; i+=2) //Make sure to increment by 2, currently ignores a trailing char.
{
string hex = text.Substring(i * 2, 2);
data[i / 2] = Convert.ToByte(hex, 16);
}
return data;
}
Not the cleanest code, but you get the idea.
You should wrap the data[i / 2] = Convert.ToByte(hex, 16); line in a try catch, but I am not sure if you want to do that for the line or just call the method in a try catch.
The problem with your code seems to be the lines x = Convert.ToInt32(text[2 * i + 1]); and y = Convert.ToInt32(text[2 * i]); which are converting the char directly to an int. to get your solution to work you should do something like x = ((byte)text[2 * i + 1]) - 48;

Your call to Convert.ToInt32() isn't doing what you think it's doing.
Here's an overview on different usages of Convert.ToInt32():
http://msdn.microsoft.com/en-us/library/bb311038.aspx
There are three problems with the logic:
Look at your if statements that determine if x and y fall within certain number ranges. Consider what happens if x = 100. Remember that || means "OR".
The conversion if x or y is a character representing a number using Convert.ToInt32() needs to take a string, not a character, in order to get the conversion you're looking for.
Once you get past those two, examine your output of your conversion() method. You should notice the final issue.

How to convert integer to binary string in C#?

I'm writing a number converter. How can I convert a integer to a binary string in C# WITHOUT using built-in functions (Convert.ToString does different things based on the value given)?
Binary -> Sign magnitude
Binary -> One's complement
Binary > Two's complement

Simple soution:
IntToBinValue = Convert.ToString(6, 2);

Almost all computers today use two's complement representation internally, so if you do a straightforward conversion like this, you'll get the two's complement string:
public string Convert(int x) {
char[] bits = new char[32];
int i = 0;
while (x != 0) {
bits[i++] = (x & 1) == 1 ? '1' : '0';
x >>= 1;
}
Array.Reverse(bits, 0, i);
return new string(bits);
}
That's your basis for the remaining two conversions. For sign-magnitude, simply extract the sign beforehand and convert the absolute value:
byte sign;
if (x < 0) {
sign = '1';
x = -x;
} else {
sign = '0';
}
string magnitude = Convert(x);
For one's complement, subtract one if the number is negative:
if (x < 0)
x--;
string onec = Convert(x);

At least part of the answer is to use decimal.GetBits(someValue) to convert the decimal to its binary representation.
BitConverter.GetBytes can be used, in turn, on the elements returned from decimal.GetBits() to convert integers into bytes.
You may find the decimal.GetBits() documentation useful.
I'm not sure how to go from bytes to decimal, though.
Update: Based on Author's update:
BitConverter contains methods for converting numbers to bytes, which is convenient for getting the binary representation. The GetBytes() and ToInt32() methods are convenient for conversions in each direction. The ToString() overloads are convenient for creating a hexadecimal string representation if you would find that easier to interpret as 1's and 0's.

var a = Convert.ToString(4, 2).PadLeft(8, '0');

Here's mine:
(The upper part convert 32-char binary string to 32-bit integer, the lower part convert 32-bit integer back to 32-char binary string).
Hope this helps.
string binaryString = "011100100111001001110011";
int G = 0;
for (int i = 0; i < binaryString.Length; i++)
G += (int)((binaryString[binaryString.Length - (i + 1)] & 1) << (i % 32));
Console.WriteLine(G); //‭7500403‬
binaryString = string.Empty;
for (int i = 31; i >= 0; i--)
{
binaryString += (char)(((G & (1 << (i % 32))) >> (i % 32)) | 48);
}
Console.WriteLine(binaryString); //00000000011100100111001001110011

You can construct the representations digit by digit from first principles.
Not sure what built-in functions you don't want to use, but presumably you can construct a string character by character?
Start with the highest power of two greater than the number.
Push a "1" into your string.
Subtract that power of two from your number.
Take the next-lowest power of two. If you've reached one-half, stop. You're done.
If the number that's left is greater than this power of two, go back to step 2. If not, push a "0" into the string and go back to step 4.
For one's complement and two's complement, calculate those with an additional step.
Or is this way too basic for what you need?

This is an unsafe implementation:
private static unsafe byte[] GetDecimalBytes(decimal d)
{
byte* dp = (byte*) &d;
byte[] result = new byte[sizeof(decimal)];
for (int i = 0; i < sizeof(decimal); i++, dp++)
{
result[i] = *dp;
}
return result;
}
And here is reverting back:
private static unsafe decimal GetDecimal(Byte[] bytes)
{
if (bytes == null)
throw new ArgumentNullException("bytes");
if (bytes.Length != sizeof(decimal))
throw new ArgumentOutOfRangeException("bytes", "length must be 16");
decimal d = 0;
byte* dp = (byte*)&d;
byte[] result = new byte[sizeof(decimal)];
for (int i = 0; i < sizeof(decimal); i++, dp++)
{
*dp = bytes[i];
}
return d;
}

Here is an elegant solution:
// Convert Integer to binary and return as string
private static string GetBinaryString(Int32 n)
{
char[] b = new char[sizeof(Int32) * 8];
for (int i = 0; i < b.Length; i++)
b[b.Length-1 - i] = ((n & (1 << i)) != 0) ? '1' : '0';
return new string(b).TrimStart('0');
}

How to convert a column number (e.g. 127) into an Excel column (e.g. AA)

How do you convert a numerical number to an Excel column name in C# without using automation getting the value directly from Excel.
Excel 2007 has a possible range of 1 to 16384, which is the number of columns that it supports. The resulting values should be in the form of excel column names, e.g. A, AA, AAA etc.

Here's how I do it:
private string GetExcelColumnName(int columnNumber)
{
string columnName = "";
while (columnNumber > 0)
{
int modulo = (columnNumber - 1) % 26;
columnName = Convert.ToChar('A' + modulo) + columnName;
columnNumber = (columnNumber - modulo) / 26;
}
return columnName;
}

If anyone needs to do this in Excel without VBA, here is a way:
=SUBSTITUTE(ADDRESS(1;colNum;4);"1";"")
where colNum is the column number
And in VBA:
Function GetColumnName(colNum As Integer) As String
Dim d As Integer
Dim m As Integer
Dim name As String
d = colNum
name = ""
Do While (d > 0)
m = (d - 1) Mod 26
name = Chr(65 + m) + name
d = Int((d - m) / 26)
Loop
GetColumnName = name
End Function

You might need conversion both ways, e.g from Excel column adress like AAZ to integer and from any integer to Excel. The two methods below will do just that. Assumes 1 based indexing, first element in your "arrays" are element number 1.
No limits on size here, so you can use adresses like ERROR and that would be column number 2613824 ...
public static string ColumnAdress(int col)
{
if (col <= 26) {
return Convert.ToChar(col + 64).ToString();
}
int div = col / 26;
int mod = col % 26;
if (mod == 0) {mod = 26;div--;}
return ColumnAdress(div) + ColumnAdress(mod);
}
public static int ColumnNumber(string colAdress)
{
int[] digits = new int[colAdress.Length];
for (int i = 0; i < colAdress.Length; ++i)
{
digits[i] = Convert.ToInt32(colAdress[i]) - 64;
}
int mul=1;int res=0;
for (int pos = digits.Length - 1; pos >= 0; --pos)
{
res += digits[pos] * mul;
mul *= 26;
}
return res;
}

Sorry, this is Python instead of C#, but at least the results are correct:
def ColIdxToXlName(idx):
if idx < 1:
raise ValueError("Index is too small")
result = ""
while True:
if idx > 26:
idx, r = divmod(idx - 1, 26)
result = chr(r + ord('A')) + result
else:
return chr(idx + ord('A') - 1) + result
for i in xrange(1, 1024):
print "%4d : %s" % (i, ColIdxToXlName(i))

I discovered an error in my first post, so I decided to sit down and do the the math. What I found is that the number system used to identify Excel columns is not a base 26 system, as another person posted. Consider the following in base 10. You can also do this with the letters of the alphabet.
Space:.........................S1, S2, S3 : S1, S2, S3
....................................0, 00, 000 :.. A, AA, AAA
....................................1, 01, 001 :.. B, AB, AAB
.................................... …, …, … :.. …, …, …
....................................9, 99, 999 :.. Z, ZZ, ZZZ
Total states in space: 10, 100, 1000 : 26, 676, 17576
Total States:...............1110................18278
Excel numbers columns in the individual alphabetical spaces using base 26. You can see that in general, the state space progression is a, a^2, a^3, … for some base a, and the total number of states is a + a^2 + a^3 + … .
Suppose you want to find the total number of states A in the first N spaces. The formula for doing so is A = (a)(a^N - 1 )/(a-1). This is important because we need to find the space N that corresponds to our index K. If I want to find out where K lies in the number system I need to replace A with K and solve for N. The solution is N = log{base a} (A (a-1)/a +1). If I use the example of a = 10 and K = 192, I know that N = 2.23804… . This tells me that K lies at the beginning of the third space since it is a little greater than two.
The next step is to find exactly how far in the current space we are. To find this, subtract from K the A generated using the floor of N. In this example, the floor of N is two. So, A = (10)(10^2 – 1)/(10-1) = 110, as is expected when you combine the states of the first two spaces. This needs to be subtracted from K because these first 110 states would have already been accounted for in the first two spaces. This leaves us with 82 states. So, in this number system, the representation of 192 in base 10 is 082.
The C# code using a base index of zero is
private string ExcelColumnIndexToName(int Index)
{
string range = string.Empty;
if (Index < 0 ) return range;
int a = 26;
int x = (int)Math.Floor(Math.Log((Index) * (a - 1) / a + 1, a));
Index -= (int)(Math.Pow(a, x) - 1) * a / (a - 1);
for (int i = x+1; Index + i > 0; i--)
{
range = ((char)(65 + Index % a)).ToString() + range;
Index /= a;
}
return range;
}
//Old Post
A zero-based solution in C#.
private string ExcelColumnIndexToName(int Index)
{
string range = "";
if (Index < 0 ) return range;
for(int i=1;Index + i > 0;i=0)
{
range = ((char)(65 + Index % 26)).ToString() + range;
Index /= 26;
}
if (range.Length > 1) range = ((char)((int)range[0] - 1)).ToString() + range.Substring(1);
return range;
}

This answer is in javaScript:
function getCharFromNumber(columnNumber){
var dividend = columnNumber;
var columnName = "";
var modulo;
while (dividend > 0)
{
modulo = (dividend - 1) % 26;
columnName = String.fromCharCode(65 + modulo).toString() + columnName;
dividend = parseInt((dividend - modulo) / 26);
}
return columnName;
}

Easy with recursion.
public static string GetStandardExcelColumnName(int columnNumberOneBased)
{
int baseValue = Convert.ToInt32('A');
int columnNumberZeroBased = columnNumberOneBased - 1;
string ret = "";
if (columnNumberOneBased > 26)
{
ret = GetStandardExcelColumnName(columnNumberZeroBased / 26) ;
}
return ret + Convert.ToChar(baseValue + (columnNumberZeroBased % 26) );
}

I'm surprised all of the solutions so far contain either iteration or recursion.
Here's my solution that runs in constant time (no loops). This solution works for all possible Excel columns and checks that the input can be turned into an Excel column. Possible columns are in the range [A, XFD] or [1, 16384]. (This is dependent on your version of Excel)
private static string Turn(uint col)
{
if (col < 1 || col > 16384) //Excel columns are one-based (one = 'A')
throw new ArgumentException("col must be >= 1 and <= 16384");
if (col <= 26) //one character
return ((char)(col + 'A' - 1)).ToString();
else if (col <= 702) //two characters
{
char firstChar = (char)((int)((col - 1) / 26) + 'A' - 1);
char secondChar = (char)(col % 26 + 'A' - 1);
if (secondChar == '#') //Excel is one-based, but modulo operations are zero-based
secondChar = 'Z'; //convert one-based to zero-based
return string.Format("{0}{1}", firstChar, secondChar);
}
else //three characters
{
char firstChar = (char)((int)((col - 1) / 702) + 'A' - 1);
char secondChar = (char)((col - 1) / 26 % 26 + 'A' - 1);
char thirdChar = (char)(col % 26 + 'A' - 1);
if (thirdChar == '#') //Excel is one-based, but modulo operations are zero-based
thirdChar = 'Z'; //convert one-based to zero-based
return string.Format("{0}{1}{2}", firstChar, secondChar, thirdChar);
}
}

Same implementation in Java
public String getExcelColumnName (int columnNumber)
{
int dividend = columnNumber;
int i;
String columnName = "";
int modulo;
while (dividend > 0)
{
modulo = (dividend - 1) % 26;
i = 65 + modulo;
columnName = new Character((char)i).toString() + columnName;
dividend = (int)((dividend - modulo) / 26);
}
return columnName;
}

int nCol = 127;
string sChars = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
string sCol = "";
while (nCol >= 26)
{
int nChar = nCol % 26;
nCol = (nCol - nChar) / 26;
// You could do some trick with using nChar as offset from 'A', but I am lazy to do it right now.
sCol = sChars[nChar] + sCol;
}
sCol = sChars[nCol] + sCol;
Update: Peter's comment is right. That's what I get for writing code in the browser. :-) My solution was not compiling, it was missing the left-most letter and it was building the string in reverse order - all now fixed.
Bugs aside, the algorithm is basically converting a number from base 10 to base 26.
Update 2: Joel Coehoorn is right - the code above will return AB for 27. If it was real base 26 number, AA would be equal to A and the next number after Z would be BA.
int nCol = 127;
string sChars = "0ABCDEFGHIJKLMNOPQRSTUVWXYZ";
string sCol = "";
while (nCol > 26)
{
int nChar = nCol % 26;
if (nChar == 0)
nChar = 26;
nCol = (nCol - nChar) / 26;
sCol = sChars[nChar] + sCol;
}
if (nCol != 0)
sCol = sChars[nCol] + sCol;

..And converted to php:
function GetExcelColumnName($columnNumber) {
$columnName = '';
while ($columnNumber > 0) {
$modulo = ($columnNumber - 1) % 26;
$columnName = chr(65 + $modulo) . $columnName;
$columnNumber = (int)(($columnNumber - $modulo) / 26);
}
return $columnName;
}

Just throwing in a simple two-line C# implementation using recursion, because all the answers here seem far more complicated than necessary.
/// <summary>
/// Gets the column letter(s) corresponding to the given column number.
/// </summary>
/// <param name="column">The one-based column index. Must be greater than zero.</param>
/// <returns>The desired column letter, or an empty string if the column number was invalid.</returns>
public static string GetColumnLetter(int column) {
if (column < 1) return String.Empty;
return GetColumnLetter((column - 1) / 26) + (char)('A' + (column - 1) % 26);
}

Although there are already a bunch of valid answers1, none get into the theory behind it.
Excel column names are bijective base-26 representations of their number. This is quite different than an ordinary base 26 (there is no leading zero), and I really recommend reading the Wikipedia entry to grasp the differences. For example, the decimal value 702 (decomposed in 26*26 + 26) is represented in "ordinary" base 26 by 110 (i.e. 1x26^2 + 1x26^1 + 0x26^0) and in bijective base-26 by ZZ (i.e. 26x26^1 + 26x26^0).
Differences aside, bijective numeration is a positional notation, and as such we can perform conversions using an iterative (or recursive) algorithm which on each iteration finds the digit of the next position (similarly to an ordinary base conversion algorithm).
The general formula to get the digit at the last position (the one indexed 0) of the bijective base-k representation of a decimal number m is (f being the ceiling function minus 1):
m - (f(m / k) * k)
The digit at the next position (i.e. the one indexed 1) is found by applying the same formula to the result of f(m / k). We know that for the last digit (i.e. the one with the highest index) f(m / k) is 0.
This forms the basis for an iteration that finds each successive digit in bijective base-k of a decimal number. In pseudo-code it would look like this (digit() maps a decimal integer to its representation in the bijective base -- e.g. digit(1) would return A in bijective base-26):
fun conv(m)
q = f(m / k)
a = m - (q * k)
if (q == 0)
return digit(a)
else
return conv(q) + digit(a);
So we can translate this to C#2 to get a generic3 "conversion to bijective base-k" ToBijective() routine:
class BijectiveNumeration {
private int baseK;
private Func<int, char> getDigit;
public BijectiveNumeration(int baseK, Func<int, char> getDigit) {
this.baseK = baseK;
this.getDigit = getDigit;
}
public string ToBijective(double decimalValue) {
double q = f(decimalValue / baseK);
double a = decimalValue - (q * baseK);
return ((q > 0) ? ToBijective(q) : "") + getDigit((int)a);
}
private static double f(double i) {
return (Math.Ceiling(i) - 1);
}
}
Now for conversion to bijective base-26 (our "Excel column name" use case):
static void Main(string[] args)
{
BijectiveNumeration bijBase26 = new BijectiveNumeration(
26,
(value) => Convert.ToChar('A' + (value - 1))
);
Console.WriteLine(bijBase26.ToBijective(1)); // prints "A"
Console.WriteLine(bijBase26.ToBijective(26)); // prints "Z"
Console.WriteLine(bijBase26.ToBijective(27)); // prints "AA"
Console.WriteLine(bijBase26.ToBijective(702)); // prints "ZZ"
Console.WriteLine(bijBase26.ToBijective(16384)); // prints "XFD"
}
Excel's maximum column index is 16384 / XFD, but this code will convert any positive number.
As an added bonus, we can now easily convert to any bijective base. For example for bijective base-10:
static void Main(string[] args)
{
BijectiveNumeration bijBase10 = new BijectiveNumeration(
10,
(value) => value < 10 ? Convert.ToChar('0'+value) : 'A'
);
Console.WriteLine(bijBase10.ToBijective(1)); // prints "1"
Console.WriteLine(bijBase10.ToBijective(10)); // prints "A"
Console.WriteLine(bijBase10.ToBijective(123)); // prints "123"
Console.WriteLine(bijBase10.ToBijective(20)); // prints "1A"
Console.WriteLine(bijBase10.ToBijective(100)); // prints "9A"
Console.WriteLine(bijBase10.ToBijective(101)); // prints "A1"
Console.WriteLine(bijBase10.ToBijective(2010)); // prints "19AA"
}
1 This generic answer can eventually be reduced to the other, correct, specific answers, but I find it hard to fully grasp the logic of the solutions without the formal theory behind bijective numeration in general. It also proves its correctness nicely. Additionally, several similar questions link back to this one, some being language-agnostic or more generic. That's why I thought the addition of this answer was warranted, and that this question was a good place to put it.
2 C# disclaimer: I implemented an example in C# because this is what is asked here, but I have never learned nor used the language. I have verified it does compile and run, but please adapt it to fit the language best practices / general conventions, if necessary.
3 This example only aims to be correct and understandable ; it could and should be optimized would performance matter (e.g. with tail-recursion -- but that seems to require trampolining in C#), and made safer (e.g. by validating parameters).

I wanted to throw in my static class I use, for interoping between col index and col Label. I use a modified accepted answer for my ColumnLabel Method
public static class Extensions
{
public static string ColumnLabel(this int col)
{
var dividend = col;
var columnLabel = string.Empty;
int modulo;
while (dividend > 0)
{
modulo = (dividend - 1) % 26;
columnLabel = Convert.ToChar(65 + modulo).ToString() + columnLabel;
dividend = (int)((dividend - modulo) / 26);
}
return columnLabel;
}
public static int ColumnIndex(this string colLabel)
{
// "AD" (1 * 26^1) + (4 * 26^0) ...
var colIndex = 0;
for(int ind = 0, pow = colLabel.Count()-1; ind < colLabel.Count(); ++ind, --pow)
{
var cVal = Convert.ToInt32(colLabel[ind]) - 64; //col A is index 1
colIndex += cVal * ((int)Math.Pow(26, pow));
}
return colIndex;
}
}
Use this like...
30.ColumnLabel(); // "AD"
"AD".ColumnIndex(); // 30

private String getColumn(int c) {
String s = "";
do {
s = (char)('A' + (c % 26)) + s;
c /= 26;
} while (c-- > 0);
return s;
}
Its not exactly base 26, there is no 0 in the system. If there was, 'Z' would be followed by 'BA' not by 'AA'.

if you just want it for a cell formula without code, here's a formula for it:
IF(COLUMN()>=26,CHAR(ROUND(COLUMN()/26,1)+64)&CHAR(MOD(COLUMN(),26)+64),CHAR(COLUMN()+64))

In Delphi (Pascal):
function GetExcelColumnName(columnNumber: integer): string;
var
dividend, modulo: integer;
begin
Result := '';
dividend := columnNumber;
while dividend > 0 do begin
modulo := (dividend - 1) mod 26;
Result := Chr(65 + modulo) + Result;
dividend := (dividend - modulo) div 26;
end;
end;

A little late to the game, but here's the code I use (in C#):
private static readonly string _Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
public static int ColumnNameParse(string value)
{
// assumes value.Length is [1,3]
// assumes value is uppercase
var digits = value.PadLeft(3).Select(x => _Alphabet.IndexOf(x));
return digits.Aggregate(0, (current, index) => (current * 26) + (index + 1));
}

In perl, for an input of 1 (A), 27 (AA), etc.
sub excel_colname {
my ($idx) = #_; # one-based column number
--$idx; # zero-based column index
my $name = "";
while ($idx >= 0) {
$name .= chr(ord("A") + ($idx % 26));
$idx = int($idx / 26) - 1;
}
return scalar reverse $name;
}

Though I am late to the game, Graham's answer is far from being optimal. Particularly, you don't have to use the modulo, call ToString() and apply (int) cast. Considering that in most cases in C# world you would start numbering from 0, here is my revision:
public static string GetColumnName(int index) // zero-based
{
const byte BASE = 'Z' - 'A' + 1;
string name = String.Empty;
do
{
name = Convert.ToChar('A' + index % BASE) + name;
index = index / BASE - 1;
}
while (index >= 0);
return name;
}

More than 30 solutions already, but here's my one-line C# solution...
public string IntToExcelColumn(int i)
{
return ((i<16926? "" : ((char)((((i/26)-1)%26)+65)).ToString()) + (i<2730? "" : ((char)((((i/26)-1)%26)+65)).ToString()) + (i<26? "" : ((char)((((i/26)-1)%26)+65)).ToString()) + ((char)((i%26)+65)));
}

After looking at all the supplied Versions here, I decided to do one myself, using recursion.
Here is my vb.net Version:
Function CL(ByVal x As Integer) As String
If x >= 1 And x <= 26 Then
CL = Chr(x + 64)
Else
CL = CL((x - x Mod 26) / 26) & Chr((x Mod 26) + 1 + 64)
End If
End Function

Refining the original solution (in C#):
public static class ExcelHelper
{
private static Dictionary<UInt16, String> l_DictionaryOfColumns;
public static ExcelHelper() {
l_DictionaryOfColumns = new Dictionary<ushort, string>(256);
}
public static String GetExcelColumnName(UInt16 l_Column)
{
UInt16 l_ColumnCopy = l_Column;
String l_Chars = "0ABCDEFGHIJKLMNOPQRSTUVWXYZ";
String l_rVal = "";
UInt16 l_Char;
if (l_DictionaryOfColumns.ContainsKey(l_Column) == true)
{
l_rVal = l_DictionaryOfColumns[l_Column];
}
else
{
while (l_ColumnCopy > 26)
{
l_Char = l_ColumnCopy % 26;
if (l_Char == 0)
l_Char = 26;
l_ColumnCopy = (l_ColumnCopy - l_Char) / 26;
l_rVal = l_Chars[l_Char] + l_rVal;
}
if (l_ColumnCopy != 0)
l_rVal = l_Chars[l_ColumnCopy] + l_rVal;
l_DictionaryOfColumns.ContainsKey(l_Column) = l_rVal;
}
return l_rVal;
}
}

Here is an Actionscript version:
private var columnNumbers:Array = ['A', 'B', 'C', 'D', 'E', 'F' , 'G', 'H', 'I', 'J', 'K' ,'L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z'];
private function getExcelColumnName(columnNumber:int) : String{
var dividend:int = columnNumber;
var columnName:String = "";
var modulo:int;
while (dividend > 0)
{
modulo = (dividend - 1) % 26;
columnName = columnNumbers[modulo] + columnName;
dividend = int((dividend - modulo) / 26);
}
return columnName;
}

JavaScript Solution
/**
* Calculate the column letter abbreviation from a 1 based index
* #param {Number} value
* #returns {string}
*/
getColumnFromIndex = function (value) {
var base = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'.split('');
var remainder, result = "";
do {
remainder = value % 26;
result = base[(remainder || 26) - 1] + result;
value = Math.floor(value / 26);
} while (value > 0);
return result;
};

These my codes to convert specific number (index start from 1) to Excel Column.
public static string NumberToExcelColumn(uint number)
{
uint originalNumber = number;
uint numChars = 1;
while (Math.Pow(26, numChars) < number)
{
numChars++;
if (Math.Pow(26, numChars) + 26 >= number)
{
break;
}
}
string toRet = "";
uint lastValue = 0;
do
{
number -= lastValue;
double powerVal = Math.Pow(26, numChars - 1);
byte thisCharIdx = (byte)Math.Truncate((columnNumber - 1) / powerVal);
lastValue = (int)powerVal * thisCharIdx;
if (numChars - 2 >= 0)
{
double powerVal_next = Math.Pow(26, numChars - 2);
byte thisCharIdx_next = (byte)Math.Truncate((columnNumber - lastValue - 1) / powerVal_next);
int lastValue_next = (int)Math.Pow(26, numChars - 2) * thisCharIdx_next;
if (thisCharIdx_next == 0 && lastValue_next == 0 && powerVal_next == 26)
{
thisCharIdx--;
lastValue = (int)powerVal * thisCharIdx;
}
}
toRet += (char)((byte)'A' + thisCharIdx + ((numChars > 1) ? -1 : 0));
numChars--;
} while (numChars > 0);
return toRet;
}
My Unit Test:
[TestMethod]
public void Test()
{
Assert.AreEqual("A", NumberToExcelColumn(1));
Assert.AreEqual("Z", NumberToExcelColumn(26));
Assert.AreEqual("AA", NumberToExcelColumn(27));
Assert.AreEqual("AO", NumberToExcelColumn(41));
Assert.AreEqual("AZ", NumberToExcelColumn(52));
Assert.AreEqual("BA", NumberToExcelColumn(53));
Assert.AreEqual("ZZ", NumberToExcelColumn(702));
Assert.AreEqual("AAA", NumberToExcelColumn(703));
Assert.AreEqual("ABC", NumberToExcelColumn(731));
Assert.AreEqual("ACQ", NumberToExcelColumn(771));
Assert.AreEqual("AYZ", NumberToExcelColumn(1352));
Assert.AreEqual("AZA", NumberToExcelColumn(1353));
Assert.AreEqual("AZB", NumberToExcelColumn(1354));
Assert.AreEqual("BAA", NumberToExcelColumn(1379));
Assert.AreEqual("CNU", NumberToExcelColumn(2413));
Assert.AreEqual("GCM", NumberToExcelColumn(4823));
Assert.AreEqual("MSR", NumberToExcelColumn(9300));
Assert.AreEqual("OMB", NumberToExcelColumn(10480));
Assert.AreEqual("ULV", NumberToExcelColumn(14530));
Assert.AreEqual("XFD", NumberToExcelColumn(16384));
}

Sorry, this is Python instead of C#, but at least the results are correct:
def excel_column_number_to_name(column_number):
output = ""
index = column_number-1
while index >= 0:
character = chr((index%26)+ord('A'))
output = output + character
index = index/26 - 1
return output[::-1]
for i in xrange(1, 1024):
print "%4d : %s" % (i, excel_column_number_to_name(i))
Passed these test cases:
Column Number: 494286 => ABCDZ
Column Number: 27 => AA
Column Number: 52 => AZ

For what it is worth, here is Graham's code in Powershell:
function ConvertTo-ExcelColumnID {
param (
[parameter(Position = 0,
HelpMessage = "A 1-based index to convert to an excel column ID. e.g. 2 => 'B', 29 => 'AC'",
Mandatory = $true)]
[int]$index
);
[string]$result = '';
if ($index -le 0 ) {
return $result;
}
while ($index -gt 0) {
[int]$modulo = ($index - 1) % 26;
$character = [char]($modulo + [int][char]'A');
$result = $character + $result;
[int]$index = ($index - $modulo) / 26;
}
return $result;
}

Another VBA way
Public Function GetColumnName(TargetCell As Range) As String
GetColumnName = Split(CStr(TargetCell.Cells(1, 1).Address), "$")(1)
End Function

Here's my super late implementation in PHP. This one's recursive. I wrote it just before I found this post. I wanted to see if others had solved this problem already...
public function GetColumn($intNumber, $strCol = null) {
if ($intNumber > 0) {
$intRem = ($intNumber - 1) % 26;
$strCol = $this->GetColumn(intval(($intNumber - $intRem) / 26), sprintf('%s%s', chr(65 + $intRem), $strCol));
}
return $strCol;
}