Chapter 3

Chapter 3 - CGS 3269 Computer Architecture Concepts Chapter...

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1 CGS 3269 Computer Architecture Concepts Chapter 3 Boolean Algebra and Digital Logic 2 CGS 3269 Computer Architecture Concepts Chapter 3 Objectives ± Understand the relationship between Boolean logic and digital computer circuits. ± Learn how to design simple logic circuits. ± Understand how digital circuits work together to form complex computer systems.
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2 3 CGS 3269 Computer Architecture Concepts 3.1 Introduction ± In the latter part of the nineteenth century, George Boole incensed philosophers and mathematicians alike when he suggested that logical thought could be represented through mathematical equations . o How dare anyone suggest that human thought could be encapsulated and manipulated like an algebraic formula? ± Computers, as we know them today, are implementations of Boole’s Laws of Thought . o John Atanasoff and Claude Shannon were among the first to see this connection. 4 CGS 3269 Computer Architecture Concepts 3.1 Introduction ± In the middle of the twentieth century, computers were commonly known as “thinking machines” and “electronic brains.” o Many people were fearful of them. ± Nowadays, we rarely ponder the relationship between electronic digital computers and human logic. Computers are accepted as part of our lives. o Many people, however, are still fearful of them. ± In this chapter, you will learn the simplicity that constitutes the essence of the machine.
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3 5 CGS 3269 Computer Architecture Concepts 3.2 Boolean Algebra ± Boolean algebra is a mathematical system for the manipulation of variables that can have one of two values. o In formal logic, these values are “true” and “false.” o In digital systems, these values are “on” and “off,” 1 and 0, or “high” and “low.” ± Boolean expressions are created by performing operations on Boolean variables. o Common Boolean operators include AND, OR, and NOT. 6 CGS 3269 Computer Architecture Concepts 3.2 Boolean Algebra ± A Boolean operator can be completely described using a truth table. ± The truth table for the Boolean operators AND and OR are shown at the right. ± The AND operator is also known as a Boolean product. The OR operator is the Boolean sum.
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7 CGS 3269 Computer Architecture Concepts 3.2 Boolean Algebra ± The truth table for the Boolean NOT operator is shown at the right. ± The NOT operation is most often designated by an overbar. It is sometimes indicated by a prime mark ( ‘ ) or an “elbow” ( ¬ ). 8 CGS 3269 Computer Architecture Concepts 3.2 Boolean Algebra ± A Boolean function has: At least one Boolean variable, At least one Boolean operator, and At least one input from the set {0,1}. ± It produces an output that is also a member of the set {0,1}. Now you know why the binary numbering
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Chapter 3 - CGS 3269 Computer Architecture Concepts Chapter...

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