converting a string of numbers to binary

Question

If the string is "8123", I first converted the string number into its integer form 8123 and then sent this number to a function that converts it to binary. I got numbers as big as unsigned long long to work but once its passed that, the outputs are wrong. Is there a way to convert to binary by looking at each digit. ie looking a the 3, 2, 1, and 8 to convert to binary.

So rather than taking the string "999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" and turning it into a number, is there a way to look at each character in this string and turn it into binary?

Any suggestions is much appreciated

Answer 1

Pseudocode:

string binary_string = ""
#an example
number = 81

while (number != 0)
    #append the string casted value of the remainder of (number / 2) 
    #to the front of binary_string
    binary_string = str(number % 2) + binary_string
    number = number / 2

eg 81:

binary_string = str(81 % 2) + binary_string = str(1) + "" = "1"

number = 81 / 2 = 40

binary_string = str(40 % 2) + binary_string = str(0) + "1" = "01"

number = 40 / 2 = 20

binary_string = str(20 % 2) + binary_string = str(0) + "01" = "001"

number = 20 / 2 = 10

binary_string = str(10 % 2) + binary_string = str(0) + "001" = "0001"

number = 10 / 2 = 5

binary_string = str(5 % 2) + binary_string = str(1) + "0001" = "10001"

number = 5 / 2 = 2

binary_string = str(2 % 2) + binary_string = str(0) + "10001" = "010001"

number = 2 / 2 = 1

binary_string = str(1 % 2) + binary_string = str(1) + "010001" = "1010001"

81 -> "1010001"

Answer 2

string dec2bin(string in) {
    for(size_t i = 0; i < in.length(); i++)
        in[i] -= '0';
    string out;
    while(in.length()) {
        out.insert(0, 1, '0' + (in[in.length()-1]&1));
        char overflow = 0;
        if(in[0]<=1) {
            overflow = 10;
            in.erase(0);
        }
        for(size_t i = 0; i<in.length(); i++) {
            in[i] += overflow;
            overflow = 10 * (in[i]&1);
            in[i] /= 2;
        }
    }
    return out;
}