Complete function binary$\_$mul$($a$,$ b$)$ that computes the product of the binary numbers

and

using ALGORITHM $1\mathrm{.}2\mathrm{.}4$ of the "Integer Representations & Algorithms" lecture notes. No credit

will be given to functions that employ any other implementation. The function can not use built$-$

in functions that already perform some kind of binary representation or addition of binary

numbers. For example, the function implementation can not use the functions bin$()$ or

int$($a$,$ base$=2).$def binary$\_$mul$(a,b$ :

# removing all whitespace from the strings

$a=$ a$.$replace$(\text{'}\text{'},\text{'}\text{'})$

b $=$ b$.$replace$(\text{'}\text{'},\text{'}\text{'})$

# multiplication algorithm

partial$\_$products $=[]$

$i=0$ # tracks the index of the current binary bit of string $\text{'}a\text{'}$ beginning at $,r$

for bit in reversed$($a$)$:

if bit $==\text{'}1\text{'}$:

partial$\_$products.append$("""$FIXME: Append the correct object to partial prc

i $+=1$

result $={?}^{\text{'}}\text{'}$

while len$($partial$\_$products$)>0$ :

result $=$ binary$\_$add$("$FIXME: Input the correct arguments"$)$

del partial$\_$products$[0]$

return # FIXME: Return the appropriate result