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the soap bubble has to be translated into a single form. this involves two things: 1. converting each of the soap bubbles into a single string of binary digits. 2. removing the 'hiccups' or the extra digits that are added at the beginning and at the end of the translation. in other words, this soap bubble can be translated into this string of binary digits: 0 010 001 011 010 100 101 101 011 0 001 001 0 11 010 0 0 0 1 1 1 0 0 now, what i did here was to break the string into two separate strings: 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 what i have just translated is the string of the first half of the string. what's left is the second half of the string. the second half consists of 0's and 1's. these two halves represent the same string. so, to translate this second half, we would follow the same process as before. we start by using a for loop to count from 0 to the number of digits of the second half. for each of these digits, we add a 1 to the digit. this process is called 'adding 1's' or 'carrying one' the number is therefore 2, so we add a 1 to every 1, giving us 2. so, we do this for every 1: 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 to translate this, we can do this: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 and this will be our translation of the second half of the string. now, we need to take our translated string and put it back together. we do this using another for loop to start at the beginning of the first half of the original string, and do this for each of the digits in the translated string. we also remove the extra 1's that we added when we translated the first half of the string. so, this would be our final translation of this string: 0 1 0 0 0 1 1 0 0 1 1 0

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