it assumes there are procedures that will do some arithemtic. it assumes that one can concatenate strings of digits: means the string consisting of the digits in x followed by those in y. it works by repeatedly setting new values to u,v,bot, yop, and side as rom rthe digits of th input are worked through in pairs from left to right. Figure out what the procedure PROCX is doing. Hint :Trace its behavior when the input is 137641. Procedure PROCX: you are given a sequence of digits X as input. you are given a sequence of digits as output. 1: Group the digits in x into pairs starting from the right.(if X has an odd number of digits, the leftmost group will only have a single digit in it.) 2:start with u,v,bot,top, and side all having an inital value of 0. 3: then working you way from the left to right on the group in X, repeat the following: (1) Set bot to (bot - u)^(the next group from X). (2) Set side to 2*top. (3) Set v to the largest single digit such that v*(side^v)bot . (4) Set u to v*(side^v) . (5) Set top to top^ v. 4: The answer to return is the final value of top.