How do i convert a number stored in string to binary format?

You actually can use Dan Byström's answer to How to convert a gi-normous integer (in string format) to hex format? (C#), like Michael Edenfeld suggested in the comments. It will get you from your large number string to hexadecimal. I will repost his code for your convenience:

var s = "25274132531129322906392322409257377862778880";
var result = new List<byte>();
result.Add(0);
foreach (char c in s)
{
    int val = (int)(c - '0');
    for (int i = 0 ; i < result.Count ; i++)
    {
        int digit = result[i] * 10 + val;
        result[i] = (byte)(digit & 0x0F);
        val = digit >> 4;
    }
    if (val != 0)
        result.Add((byte)val);
}

var hex = "";
foreach (byte b in result)
    hex = "0123456789ABCDEF"[b] + hex;

I won't profess to understand how he came up with this, but I have tested it with a few numbers that I know the hex values for, and it appears to work. I'd love to hear an explanation from him.

Now, you want your answer in binary, and luckily for you, converting from hexadecimal to binary is one of the easier things in life. Every hex value converts directly to its 4-bit binary counterpart (0x7 = 0111, 0xA = 1010, etc). You could write a loop to perform this conversion character by character, but Guffa's answer to C# how convert large HEX string to binary provides this handy dandy Linq statement to perform the same action:

string binaryString = string.Join(string.Empty,
hex.Select(c => Convert.ToString(Convert.ToInt32(
c.ToString(), 16), 2).PadLeft(4, '0')));

Running all of this together gives me:

01110001010101010100100000000000110010010010001010100000000000000101110111000000000001010001010000000000110001111111111111111111111111111111111011100010

For your number. I don't know how you plan to verify it, but if Dan's hex translation is right, then that binary string will definitely be right.

System.Convert can help you with bits and pieces like this. See below.

string decString = "12345";
int integer = Convert.ToInt32(decString);
string binString = Convert.ToString(integer, 2);

You can try this:

string number = "25274132531129322906392322409257377862778880";
char[] strArr = number.ToCharArray();
StringBuilder sb = new StringBuilder();
foreach (char chr in strArr)
{
    sb.Append(Convert.ToString((int)Char.GetNumericValue(chr), 2));
}
string binresult = sb.ToString();