film and digital media. film and digital media.
The purpose of this exercise is to get you familiar with binary representations, formal languages and algorithms. Admittedly, all of these are huge and involved topics, but the assignment is short and hopefully easy. Remember when you learned your addition tables in elementary school? 1 + 1 = 2; 2 + 2 = 4; 9 + 7 = 16; etc. Those facts about addition are facts of decimal addition. Here are the main facts of binary addition: 0 + 0 = 0; 0 + 1 = 1; 1 + 1 = 10. Now, remember learning multiple column addition in which you add numbers with more than one digit and in which, sometimes, you had to “carry” if a column added up to 10 or more? That procedure of multiple column addition can be called an “algorithm.” The algorithm can be stated in a set of rules written in a formal language; e.g., if the integer in the first row is comprised of a series of digits, xyz, and the integer in the second row is comprised of a series of digits, qrs, then to add the two integers together first find the sum of z + s = w; if, w > 9, then w has two digits c and d; write d in the third row, carry c to a row above the first row, now repeat the steps above by adding the digits c + y + r, and so forth. I want you to do something like the above, but note that my description is inadequate both because I am only dealing with integers of three digits while the algorithm should be applicable to integers with any number of digits and also it is inadequate from the perspective of a formal language because I still need to define what a row is, what a column is, what the facts of binary addition are, what it means to say “repeat the steps above” or “and so forth,” etc. For those of you who know how to computer program, the easiest way to complete this assignment will simply be to write a piece of code that adds two binary numbers together. Assume the binary numbers are given to you as string, not as bit vectors. Write the code using strings and not bit vectors as a representation for the binary integers. For those of you who do not know how to program, the easiest way to complete this assignment will be for you to think back to elementary school and try to reproduce the instructions your teachers gave you when you were learning how to add decimal numbers (and translate those instructions so that they work for binary numbers). Yes, you can include diagrams in your explanations if you think, for example, that that will be the easiest way to define what a row or a column of digits is. Your list and description of the rules of binary addition should take no more than a page of text and/or diagrams.p(1)
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