As the name “computer” implies, a major task of these machines is to do arithmetic computation. Every method of computation is based on an algorithm, or a familiar set of steps to get the result. However, computers are optimized for speed, and therefore do not use the same algorithms that we learn in school. The Computation unit begins with a review and explanation of how multi-digit addition is usually done. The standard algorithm uses the “carry” to regroup the leading digit of sums that are too large to fit into the current column. This algorithm requires you to proceed from right to left, because the carried amount is unknown in any other sequence. An alternative algorithm is the Mexican Folk Algorithm, also called Partial Sums, which can proceed in any direction. The result of each column is recorded, and these partial sums are then added together at the end. Students learn and experiment with this method and then compare it to the standard algorithm. To save time and hardware, computers use a partial sum to add binary numbers. In this case, each column is added without the carry bits, which are recorded in the row below. The two rows are then added together to get the result. One advantage is that all the columns are added in any order, or even simultaneously. Another is that an adder circuit requires only two inputs, unlike the standard algorithm, which requires three, including the incoming carry.

Computation Curriculum