# Numerical computations in C++ : Converting from Decimal to Binary – 2

Earlier we looked at a recursive method for conversion from decimal to binary. We can also achieve the conversion in an iterative manner, however adding to the task the additional overhead of reversing the answer that we obtain.

The underlying method is the one discussed at the beginning of the previous post. At each iteration, we divide a number by 2 and store the corresponding remainder in an array. At the end of the process, we reverse the contents of the array.

Now, we are faced with a small problem. How do we know what the size of our array should be? Fortunately, we can proceed without knowing that, using the resizeable vector container class. (A vector is like a dynamic array. We need not specify its size at the time of definition.)

In order to reverse the vector, we can simply use the reverse algorithm defined in the algorithm header. Or if we simply want to output the binary representation (without needing to store it anywhere), we may simply use a reverse_iterator to iterate through our vector.

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// function dec_to_bin outputs the binary equivalent of the decimal input n.

#include <iostream>

#include <vector>

using namespace std;

void dec_to_bin ( int n )

{

vector <int> v; // vector of ints to store the binary representation.

int temp = n;

if ( n < 0)

temp = -n;

while ( temp != 0)

{

v.push_back (temp%2);

temp / = 2;

}

vector<int> reverse_iterator i;

if ( n < 0)

cout << ” – ” ;

for ( i = v.rend ( ); i != v.rbegin ( ); ++i)

cout << *i;

}

——-

If we used a list or a deque instead of a vector, we wouldn’t be faced with the task of having to reverse the values computed by us. We can do this by storing successive numbers that we generate at the front of the data structure instead of at the end.

We may do that using the push_front member function for lists and deques. (Note that we cannot use push_front for a vector. We can only insert and delete elements (efficiently i.e. in constant time) at the back of a vector.)

——

The above program using a deque along with push_front would look as follows:

——

#include <iostream>

#include <deque>

#include <algorithm>

using namespace std;

void dec_to_bin ( int n )

{

deque <int> v;

int temp = n;

if ( n < 0)

temp = -n;

while (temp != 0)

{

v.push_front ( temp%2);

temp /=2;

}

if ( n < 0)

cout << “-“;

copy (v.begin( ), v.end ( ), ostream_iterator<int> (cout,””);

}

——-

Instead of using an iterator to iterate through the deque, we can use the copy algorithm defined in the header algorithm to directly output the contents of the deque. (Note that the statement #include <algorithm> though written as part of the above program is not necessary, since algorithm.h automatically gets included when we write #include <deque>. )

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