Fast way to convert a binary number to a decimal number

Question

I have to convert a binary number like for example unsigned int bin_number = 10101010 into its decimal representation (ie 170 ) as quickly as possible? What is the best algorithm?

Answer 1

Using templates you can solve this problem at compile-time .

template<unsigned long num>
struct binary
{
    static unsigned const value =
        binary<num/10>::value << 1 | num % 10;
};

// Specialization for zero
template<>
struct binary<0>
{ static unsigned const value = 0; };

The binary template is instantiated again with a smaller num , until num reaches zero and the specialization is used as a termination condition.

Example: std::cout << binary<10101010>::value;

For run-time problem:

unsigned binary_to_decimal(unsigned num)
{
    unsigned res = 0;

    for(int i = 0; num > 0; ++i)
    {
        if((num % 10) == 1)
            res += (1 << i);

        num /= 10;
    }

    return res;
}

Answer 2

Well, if this "number" is actually a string gotten from some source (read from a file or from a user) that you converted into a number (thinking it to be more appropriate for an actual number), which is quite likely, you can use a std::bitset to do the conversion:

#include <bitset>

unsigned int number = std::bitset<32>("10101010").to_ulong();

(Of course the 32 here is implementation-defined and might be more appropriately written as std::numeric_limits<unsigned int>::digits .)

But if it is really a number (integer variable) in the (very) first place you could do:

#include <string>

unsigned int number = std::bitset<32>(std::to_string(bin_number)).to_ulong();

(using C++11's to_string ) But this will probably not be the most efficient way anymore, as others have presented more efficient algorithms based on numbers. But as said, I doubt that you really get this number as an actual integer variable in the very first place, but rather read it from some text file or from the user.

Answer 3

Actually if you write unsigned int bin_number = 10101010 , this is interpreted as a decimal number by the compiler.

If you want to write a binary literal in your source code, you should use BOOST_BINARY . Then, you just need to print it using cout , decimal is the default...

unsigned int i = BOOST_BINARY(10101010);
std::cout << i; // This prints 170

Answer 4

Since C++11 (even if C++11 is more limited than C++14 in that regard), function can be constexpr so avoid necessity of template to have compile time value.

Here a version C++14 compatible:

constexpr unsigned binary_to_decimal(unsigned num)
{
    unsigned res = 0;

    while (num)
    {
        res = 10 * res + num % 10;
        num /= 10;
    }
    return res;
}

And for literals, you can even use binary literals since C++14:

0b1010'1010 // or 0b10101010 without separator

Answer 5

If you know the number of binary digits that you're dealing with and it's always fixed and the binary number comes in a string (as it would if read from a file or stdin) at runtime (ie compile time conversion not possible) then you could adopt this approach:

int to_binary( const char* c )
{
    return ( ( c[0] & 1 ) ? 0x80 : 0x00 ) |
           ( ( c[1] & 1 ) ? 0x40 : 0x00 ) |
           ( ( c[2] & 1 ) ? 0x20 : 0x00 ) |
           ( ( c[3] & 1 ) ? 0x10 : 0x00 ) |
           ( ( c[4] & 1 ) ? 0x08 : 0x00 ) |
           ( ( c[5] & 1 ) ? 0x04 : 0x00 ) |
           ( ( c[6] & 1 ) ? 0x02 : 0x00 ) |
           ( ( c[7] & 1 ) ? 0x01 : 0x00 );
}

This assumes an fixed eight digit binary number. called like this:

std::cout << to_binary("10101010") << std::endl;

If you had a sixteen bit number you could still use it:

const char* bin_number = "1010101010101010";

// Deal with 16 bits
std::cout << ( to_binary( bin_number ) << 8 | to_binary( bin_number + 8 ) ) << std::endl;

Note that there is clearly no bounds checking here and I'm relying on the fact that the LSB of '1' is always 1 and '0' is always 0 (so not validating that it's actually a binary input.)

Naturally, it's pretty specific and not very flexible, but it does the job and I'm not sure that you'd get much faster.