Implementation of a Four-bit Adding Machine Bryanna Davison, Kristopher Cotten Santa Rosa Junior College Abstract Methods Results Digital computation lies at the basis of nearly all modern pursuits of knowledge. This computation is performed utilizing only a single voltage, manipulating the voltage on or off to simulate a base two number of either a one or a zero. Numerous logic devices have sprung up to implement computations in this digital space, and most modern computers perform their computations through the use of addition and nothing else. The half adder, and consequently the full adder, make everything in the Central Processing Unit possible. Their logic may be • A logical AND gate with output • An OR Gate with its expected • The Exclusive-OR, or XOR, gate is • Users input two numbers truth table that demonstrates extended through the use of a carry out signal to output. similar to an OR gate. • Each number consists of four bits, also known another adder, all the way up to an arbitrary expected output from given inputs. • An OR operation could be said to be • The operation will only have an • as a byte amount of n bits. In the interest of minimizing An AND operation might be said to adding the two inputs together. output if A or B is high, not if both be Multiplying the two inputs • Input is adjusted through the use of toggle complexity the four-bit binary adding machine • If both inputs are high then the inputs are high. • The only way to ensure an output output will also produce a carry bit • XOR gates can model a linear switches. The switches simulate either a one or a was chosen to showcase these fundamentals of is by having two high inputs, or that is resolved with the use of an feedback shift register, in order to zero, for high and low voltage respectively computer processing. In order to realize binary ones. adder generate random numbers • A one or a zero must always be applied to the computation, a circuit design was first gate or results may become unpredictable approached through the use of a Simulation • The four-bit adder will compute the result of the Program with Integrated Circuit Emphasis • The Half Adder can provide the addition without any need for user interaction (SPICE). Once the SPICE was complete, a expected sum and carry for the • The result of the binary addition is displayed to working circuit was implemented with integrated addition of two numbers in binary the user in binary through an array of LEDs circuit logic gates on a solderless breadboard. • Can not account for a carry in bit from any previous operation • Combines with a second half adder Conclusion Introduction and an OR gate to form a full adder • The ability to add two four-bit binary numbers At the most fundamental level of all computing the • Possibility exists to emulate subtraction using one-bit adding circuit consists of a single half Gray Code adder. A second half adder can then be added to • The four-bit adder is a small step towards a account for the carry bit (that results from base Finite State Machine and other more complex two addition) transforming the adder into what is automata known as a full adder. The chosen implementation of the adder required two AND gates, two exclusive OR gates (XOR gate), and a single OR Acknowledgements • All of these calculations • A typical transistor adder gate. Once the first adder is complete the carry and are made possible schematic that uses Not AND Thanks to the Santa Rosa Junior College MESA the sum go on to become the inputs of the next through the use of gates, also known as NAND gates program and its director Darci Rosales for adder, continuing in this fashion until the circuit transistors • NAND gates are common in providing funding for this project and to Monica includes the requisite gates for four-bit addition. • Easily outputs digital commercial and industrial Acosta for poster planning and editing assistance. signals applications due to fewer wires • Has the advantages of being able to account for a Materials carry in bit • Carry in and out allows for the full adder to be References • Transistors strung together and calculate numbers with “n” Petzold, Charles. Code: The Hidden Language of • Integrated Circuits bits • In practice the adder will output in accordance Computer Hardware and Software. • Light Emitting Diodes with the truth table seen here, just as if the Redmond, WA: Microsoft Press, 2000. Print. • Resistors “numbers” had been added by hand • Jumper Wire • The logic diagram and truth table shown here can Malvino, Albert Paul, and Donald P. Leach. Digital • Toggle Switches also be implemented using diodes, relays, Principles and Applications. 2nd ed. • Breadboards software, or even with carefully crafted wood and • The Four-Bit Adder will actualize the addition of two New York: McGraw-Hill, 1975. Print. marbles • AC to DC transformer four bit binary numbers POSTER TEMPLATE BY: www.PosterPresentations.com.