class Binary: If you use any method you have defined in another method definition, use the

overloaded operator, if there is one. For instance, you will lose points if we see anything like

bin$1.\_\_$add$\_\_($bin$2).$ This should be bin$1+$ bin$2.$ Decorate your class with the

functools.total$\_$ordering decorator.

init: init has one string parameter with a default argument of $\text{'}0\text{'}.$ This string can be the empty

string $($treat the same as $\text{'}0\text{'}).$ Otherwise, it should consist only of $0$s and $1$s and should be $16$ or less

characters long. If the argument does not meet these requirements, raise a RuntimeError. Each

Binary object has one instance variable, an integer array of length $16$ called bit$\_$array.

bit$\_$array has integers $0$ or $1$ in the same order as the corresponding characters in the argument. If

the string is less than $16$ characters long, bit$\_$array should be padded on the left with the leftmost

digit in the string $($intified$,$ of course$).$ You may not use lists in this method.

eq: Takes a Binary object as an argument. Return True if self $==$ the argument, False

otherwise. You may not use int in this method. Do this one after init $$ many of the tests won't work

until this one passes.

repr: Return a $16-$character string representing the fixed$-$width binary number, such as:

$\text{'}00000000000000000\text{'}.$

add: Takes a Binary object as an argument. Return a new Binary instance that represents the sum

of self and the argument. If the sum requires more than $16$ digits, raise a RuntimeError. You may

not use int in this method.

neg: Return a new Binary instance that equals $-$self. You may not use int in this method.

sub: Takes a Binary object as an argument. Return a new Binary instance that represents self $$

the argument. You may not use int in this method.

int: Return the decimal value of the Binary object. This method should never raise a

RuntimeError due to overflow. Do not use this int on Binary objects in any other method. Do

not use the built$-$in int, either. You will probably need to use the item method on the integer that you

calculate to extract the regular Python int from the np$.$int$32$ instance that you have created.

lt: Takes a Binary object as an argument. Return True if self $<$ the argument, False

otherwise. This method should never raise a RuntimeError due to overflow. You may not use int

in this method.

abs: Return a new instance that is the absolute value of self. You may not use int in this method.