Here are the errors

Binary.cpp: In function `std::istream& operator>>(std::istream&, binary&)':

Binary.cpp:24: error: `nodeType*binary::head_ptr' is private

Binary.cpp:114: error: within this context

Binary.cpp:24: error: `nodeType*binary::head_ptr' is private

Binary.cpp:115: error: within this context

Binary.cpp:115: error: call of overloaded `list_clear(nodeType*&)' is ambiguous

Binary.cpp:28: note: candidates are: void list_clear(nodeType*&)

Binary.cpp:56: note: void list_clear(nodeType*)

Binary.cpp:24: error: `nodeType*binary::head_ptr' is private

Binary.cpp:128: error: within this context

Binary.cpp:24: error: `nodeType*binary::head_ptr' is private

Binary.cpp:130: error: within this context

#include <iostream>
#include<cstdlib>
using namespace std;

struct nodeType
{
int info;
nodeType *link;
};

class binary
{
    friend ostream& operator<<(ostream& outfile,const binary& outclass);
    friend istream& operator>>(istream& infile, const binary& inclass);
    friend binary& operator+(const binary& num1,const binary& num2);

    public:
           binary();
           binary(const binary & inclass);
           ~binary();
           const binary & operator =(const binary & otherlist);
           int getcount() const;
    private:
            nodeType *head_ptr;
            int count;
    };

void list_clear(nodeType*&head_ptr);
void list_copy(const nodeType*source_ptr, 
     nodeType*&head_ptr, nodeType*&tail_ptr);
void resetlist(nodeType * &mylist);

binary::binary()
{
    count = 0;
    head_ptr = NULL;
}
binary::binary(const binary & inclass)
{
    nodeType *tail_ptr;
    list_copy(inclass.head_ptr, head_ptr, tail_ptr);
}
binary::~binary()
{
    list_clear(head_ptr);
}
const binary & binary::operator =(const binary & otherlist)
{

}
int binary::getcount() const
{
    return count;
}
void list_clear(nodeType*head_ptr)
{
    nodeType *temp;

    while(head_ptr != NULL)
    {
    temp = head_ptr;
    head_ptr = head_ptr->link;
    delete temp;
    }
}
void list_copy(nodeType*&source_ptr, nodeType*&head_ptr, nodeType*&tail_ptr)
{
     nodeType *temp;
     head_ptr = NULL;
     tail_ptr = NULL;

     if(source_ptr == NULL)
         return;

     head_ptr = new nodeType;
     head_ptr->link = NULL;
     head_ptr->info = source_ptr->info;
     tail_ptr = head_ptr;

     source_ptr = source_ptr->link;

     while(source_ptr !=NULL)
     {
                      temp = new nodeType;
                      temp->link = NULL;
                      temp->info = source_ptr->info;
                      tail_ptr->link = temp;
                      tail_ptr = tail_ptr->link;
                      source_ptr = source_ptr->link;
     }
}
void resetlist(nodeType * &mylist)
{
    nodeType * templist;
    nodeType * tempnode;
    templist = NULL;

    while(mylist != NULL)
    {
    tempnode = mylist;
    mylist = mylist->link;
    tempnode->link = templist;
    templist = tempnode;
    }
    mylist = templist;
}
istream& operator>>(istream & infile, binary & inclass)
{
    nodeType *newNode, *temp;
    int numconv;
    char ch;

    temp = NULL;
    inclass.head_ptr = NULL;
    list_clear(inclass.head_ptr);

    infile>>ws;
    infile.get(ch);


    while(infile && isdigit(ch))
    {
    numconv = ch -'0';//Converts the number to ASCII
    newNode= new nodeType;
    newNode->info = numconv;
    newNode->link = NULL;

    if(inclass.head_ptr == NULL)
    {
         inclass.head_ptr = newNode;
    }
    else
    {
         temp->link = newNode;
    }
         temp = newNode;
         infile.get(ch);
    }
    infile>>numconv;
}
ostream& operator<<(ostream& outfile,const binary& outclass)
{

    nodeType *newNode;
    newNode = new nodeType;
    newNode = outclass.head_ptr;

    while(newNode != NULL)
    {
                  outfile<<newNode->info<< " ";
                  newNode=newNode->link;
    }
    return outfile;
}
binary& operator+(const binary& num1,const binary& num2)
{ 

}

At line 107 you are missing the const on the declaration of the inclass parameter

Your declaration and definition of list_clear at lines 28 and 55 do not match

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