$($C$++)$Refactor the Binary class to add one or more proxies to generate the desired output.

$$ Overload a COMBO combination of $$AND$,$ XOR $$ to change it$$s behavior.

o Instead of doing the binary operations do a three element addition.

o a & b $^$ c $$ a $+$ b $+$ c

$$ Do not ADD any files to the project

$$ No free functions do all overloading inside classes as methods

$$ No modern C$++$

o No Lambdas, Autos, templates, etc...

o No Boost

$$ NO Streams

o Used fopen, fread, fwrite...

$$ No code in MACROS

o Code needs to be in cpp files to see and debug it easy

$$ Exception:

o implicit problem needs templates

$//$ Binary.h

$```$cpp

#ifndef BINARY$\_$H

#define BINARY$\_$H

struct Binary

$\{$

Binary$()$;

Binary$($unsigned int $\_$x$)$;

Binary$($const Binary &r$)$;

~Binary$()$;

Binary operator $=($const Binary &r$)$;

struct XOR;

struct AND;

struct COMBO;

struct COMBO$2$;

XOR operator $^($const Binary& r$)$ const;

AND operator & $($const Binary& r$)$ const;

COMBO operator & $($const XOR& r$)$ const; $//$ TODO : Need to Fix.

operator unsigned int$()$ const;

$//$ Data: $($do not add or modify the data$)$

unsigned int x;

$\}$;

struct Binary::XOR

$\{$

XOR$($const Binary& a$,$ const Binary& b$)$;

operator Binary$()$ const;

operator unsigned int$()$ const;

const Binary& a;

const Binary& b;

$\}$;

struct Binary::AND

$\{$

AND$($const Binary& a$,$ const Binary& b$)$;

operator Binary$()$ const;

operator unsigned int$()$ const;

const Binary& a;

const Binary& b;

$\}$;

struct Binary::COMBO $\{$

COMBO$($const Binary& a$,$ const XOR& b$)$;

operator Binary$()$ const;

operator unsigned int$()$ const;

const Binary& a;

const XOR& b;

$\}$;

#endif

$//---$ End of File $---$

$```$

$//$ Binary.cpp

$```$cpp

#include "Binary.h$"$

Binary::Binary$()//$ DO NOT MODIFY

$\{$

this$->$x $=0$;

$\}$

Binary::Binary$($unsigned int $\_$x$)//$ DO NOT MODIFY

$\{$

this$->$x $=\_$x;

$\}$

Binary::Binary$($const Binary& r$)//$ DO NOT MODIFY

$\{$

this$->$x $=$ r$.$x;

$\}$

Binary::~Binary$()//$ DO NOT MODIFY

$\{$

$\}$

Binary Binary::operator $=($const Binary& r$)//$ DO NOT MODIFY

$\{$

this$->$x $=$ r$.$x;

return $*$this;

$\}$

Binary::XOR Binary::operator $^($const Binary& r$)$ const

$\{$

return XOR$(*$this$,$ r$)$;

$\}$

Binary::AND Binary::operator & $($const Binary& r$)$ const

$\{$

return AND$(*$this$,$ r$)$;

$\}$

Binary::COMBO Binary::operator & $($const XOR& r$)$ const $//$ TODO : Need to fix

$\{$

return COMBO$(*$this$,$ r$)$;

$\}$

Binary::operator unsigned int$()$ const

$\{$

return this$->$x;

$\}$

Binary::XOR::XOR$($const Binary& a$,$ const Binary& b$)$ : a$($a$),$ b$($b$)\{\}$

Binary::XOR::operator Binary$()$ const

$\{$

return Binary$($a$.$x $^$ b$.$x$)$;

$\}$

Binary::XOR::operator unsigned int$()$ const

$\{$

return a$.$x $^$ b$.$x;

$\}$

Binary::AND::AND$($const Binary& a$,$ const Binary& b$)$ : a$($a$),$ b$($b$)\{\}$

Binary::AND::operator Binary$()$ const

$\{$

return Binary$($a$.$x & b$.$x$)$;

$\}$

Binary::AND::operator unsigned int$()$ const

$\{$

return a$.$x & b$.$x;

$\}$

Binary::COMBO::COMBO$($const Binary& a$,$ const XOR& b$)$ : a$($a$),$ b$($b$)\{\}$

Binary::COMBO::operator Binary$()$ const $\{$

return Binary$($a$.$x $+$ b$.$a$.$x $+$ b$.$b$.$x$)$;

$\}$

Binary::COMBO::operator unsigned int$()$ const $\{$

return a$.$x $+$ b$.$a$.$x $+$ b$.$b$.$x;

$\}$

$//---$ End of File $---$

$```$

Sample Test Code :

$//$ Combo

Binary a$1(0$x$1)$;

Binary a$2(0$x$2)$;

Binary a$3(0$x$5)$;

Binary a$\_$Binary;

unsigned int a$\_$Value;

Binary t$\_$Binary;

unsigned int t$\_$Value;

Binary tt$\_$Binary;

unsigned int tt$\_$Value;

Trace::out$("$a$1-->0$x$\%$x

$",$ a$1.$x$)$;

Trace::out$("$a$2-->0$x$\%$x

$",$ a$2.$x$)$;

Trace::out$("$a$3-->0$x$\%$x

$",$ a$3.$x$)$;

Trace::out$("$

$")$;

a$\_$Binary $=$ a$1$ & a$2^$ a$3$;

a$\_$Value $=$ a$1$ & a$2^$ a$3$;

Trace::out$("$a$\_$Binary $=$ a$1$ & a$2^$ a$3-->0$x$\%$x

$",$ a$\_$Binary.x$)$;

Trace::out$("$a$\_$Value $=$ a$1$ & a$2^$ a$3-->0$x$\%$x

$",$ a$\_$Value$)$;

Trace::out$("$

$")$;

Sample Test Output :

a$1-->0$x$1$

a$2-->0$x$2$

a$3-->0$x$5$

a$\_$Binary $=$ a$1$ & a$2^$ a$3-->0$x$8$

a$\_$Value $=$ a$1$ & a$2^$ a$3-->0$x$8$

However, the problem currently occurring in the above code output :

a$1-->0$x$1$

a$2-->0$x$2$

a$3-->0$x$5$

a$\_$Binary $=$ a$1$ & a$2^$ a$3-->0$x$5$

a$\_$Value $=$ a$1$ & a$2^$ a$3-->0$x$5$

The test fails, $0$x$5$ is an invalid output.

If I calculate a$1$ & a$2$and a$2^$ a$3$ separately

a$1$ & a$2-->0$x$0$

a$2^$ a$3-->0$x$7$

it seems like a$2^$a$3$ should be calculated first to get the result of $0$x$8...$ but I don't know how.

Please modify the COMBO part so that I get the same result as the sample output,

a$1$ & a$2^$ a$3-->0$x$8.$

$!!!$NEVER NEVER NEVER Chenge test code to like a$1$ & $($a$2^$ a$3)!!!$