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Digital lab and Special Topics in Digital Systems Enrichment Activity 2004 NASA SHARP Program California State University, Los Angeles Presented by: Mr. Reynaldo Ruiz & Prof. Jack Levine (EE) Reported by: Fozoh Saliki
On July 23, 2004, the NASA SHARP students attended two labs at California State University, both dealing with digital circuits. Mr. Reynaldo Ruiz, electrical engineering major at California State University, taught the first, the digital logic lab. Professor Jack Levine of California State University taught the second lab, digital systems. In the first lab, Mr. Ruiz addressed topics such as integrated circuit (IC) fabrication, digital design theory, and logic gates. Professor Jack Levine continued on the topic of digital systems, drawing comparisons between switches and logic gates and teaching the students about half and full adder circuits.
IC fabrication is an exacting process consisting of many stages through which IC chips are made. Because integrated circuits are highly sensitive, this process takes place in a clean room in order to avoid contamination from dust, metals, and organic material. The stages include circuit design, pattern layout, mask manufacture, wafer processing, wafer testing, assembly, and reliability testing. Wafer processing, which creates the circuit on the wafer as part of the wafer structure, is the main stage. This stage combines such subprocesses as photolithography, thin-film formation, etching, doping, and epitaxial growth in a single cycle, and the IC chip is completed through tens of cycles.
Digital design theory is the theory that explains how digital circuits work. This theory involves topics such as binary numbers, basic conversion, Boolean algebra, and gate level minimization. Binary numbers are used by computers to represent various types of data. They differ from our common decimal numbers (base 10) in that they are base 2 and are represented with 0’s and 1’s. When converting from decimal to binary numbers, one simply divides an integer (or integer part of a number) repeatedly by two, using “remainders” rather than decimal places and writing the remainder each time, all the way down until 1. The remainders, read from bottom to top, represent the decimal number in its binary form. Boolean algebra is the system of algebra (named after the mathematician who studied it, George Bool) that is the foundation of all digital systems. This system is based on two numbers, 0 and 1, commonly thought of as “false” and “true”. There are four arithmetic operators in Boolean algebra: NOT, AND, OR, and EXCLUSIVE OR. NOT takes one input and negates it: NOT 1 is 0. AND takes two inputs and yields true if both values are true: 1 AND 1 is 1, but 1 AND 0 is 0. OR takes two inputs and yields true if at least one of the inputs is true: 0 OR 0 is 0, but 0 OR 1 is 1. EXCLUSIVE OR, or XOR, takes two inputs and yields true if only one of the inputs is true: 1 XOR 0 is 1, but 1 XOR 1 is 0. Each arithmetic operator can be represented with a logic gate. Various gate symbols are shown in Figure 1. Gate level minimization aims at simplifying digital circuits by minimizing the number of logic gates (material) that will be needed to build a circuit.
Figure 1
Various types of switches operate like digital circuits. The toggle switch, which is used in most buildings, operates like an EXCLUSIVE OR logic gate. Both ends of the switch contain the binary numbers 1 and 0, as shown in Figure 2:
Figure 2
The bulb will be lit only when one end of the switch is true (1) and the other false (0). Thus, it behaves like an EXCLUSIVE OR gate: 1 XOR 0 is true (light on), and 1 XOR 1 is false (light off).
Finally, the NASA SHARP students learned about half and full adder circuits. A half adder circuit adds two binary digits, A and B, to give a sum term, S, and a carry out term, Cout, both being Boolean variables. A full adder takes in three binary digits to produce a sum, S, and a carry out, Cout. The extra third digit in a full adder is the carry in, Cin, from a previous addition. In a half adder circuit, S = A XOR B, and Cout = A AND B. In a full adder circuit, S = A XOR B XOR Cin, and C = (A AND B) OR (B AND Cin) OR (A AND Cin). For some students, the labs were very difficult to follow. Others caught on rather quickly. But every student left the second lab with a much broader knowledge of digital circuits.
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