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es4_lab3 - Tufts University School of Engineering...

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Tufts University School of Engineering Department of Electrical and Computer Engineering ES4 - Introduction to Digital Circuits Spring 2008 Lab Section: Tuesday 3:00-6:00pm Experiment 3 2-Bit Adder Name: Teddy Portney [email protected] tufts.edu Submitted to: James Pringle Experiment Performed: March 4, 2008 Experiment Due: March 11, 2008
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I. PURPOSE The purpose of this experiment was to provide a more in-depth implementation of the hardware description language VHDL, as well as the program Xilinx ISE. This experiment also provided an opportunity to demonstrate further skill in traversing the process from a functional specification all the way to a circuit that performs the desired task. I. INTRODUCTION It is very common for engineers to be assigned a task, such as the one in this lab, which was to design two full-adder circuits and implement them by cascading them together with the end objective of adding two two-bit numbers. The process through which an engineer must travel is fairly intensive, and involves several steps. The first step requires the designing of a truth table. Since the engineer will probably be given at least a good idea of how many inputs the circuit will need, they can easily calculate the number of possible combinations for such a truth table by using the formula which states that the number of rows in a truth table is equal to 2 N , where N is the number of inputs. With some specifications, there will only be one column of outputs, which makes the rest of the process very trivial. However, in most cases, there will be more than one column, which greatly increases the amount of time needed to deduce an answer, and increases the likelihood of making an error and not noticing. After creating an accurate truth table, each column of outputs is considered its own function. Here, it is obvious why tables with one output column make life much simpler. For each output column, the function can be written in canonical form very easily by looking at the truth table. This only requires looking at where the function produces an output of “1” and writing the number of the corresponding minterm in sum-of-products form. From the SOP canonical forms of these functions, it is easy to create K-Maps, one for each function, in an attempt to minimize the functions. Again, there is a formula relating the number of squares required for the K-Map and the number of input variables. Again, this relationship is 2 N , where N is the same as in the previous formula, the number of variables. After the K-Map is filled in, largest groups of “1” ‘s
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