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Chapter 7 Logic Circuits 1. State the advantages of digital technology compared to analog technology. 2. Understand the terminology of digital circuits. 3. Convert numbers between decimal, binary, and other forms. ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits 5. Understand the binary arithmetic operations used in computers and other digital systems. 6. Interconnect logic gates of various types to implement a given logic function. 7. Use Karnaugh maps to minimize the number of gates needed to implement a logic function. ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Advantages of the Digital Approach Provided that the noise amplitude is not too large, the logic values represented by a digital signal can still be determined after noise is added. With modern IC technology, it is possible to manufacture exceedingly complex digital circuits economically. ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Definitions Positive versus Negative Logic Digital Words In parallel transmission, an n-bit word is transferred on n wires, one wire for each bit, plus a common or ground wire. In serial transmission, the successive bits of the word are transferred one after the other with a single pair of wires. ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Binary Numbers ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Gray Code ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Complement Arithmetic The one’s complement of a binary number is obtained by replacing 1s by 0s, and vice versa. 01001101 10110010 (one’s complement) ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits The two’s complement of a binary number is obtained by adding 1 to the one’s complement, neglecting the carry (if any) out of the most significant bit. Complements are useful for representing negative numbers and performing subtraction in computers. ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Subtraction Using Two’sComplement Arithmetic ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Overflow and Underflow In performing arithmetic using two’scomplement arithmetic, we must be aware of the possibility of overflow in which the result exceeds the maximum value that can be represented by the word length in use. ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Boolean algebra expressions can be implemented by interconnection of AND gates, OR gates, and inverters. ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits De Morgan’s Laws If the variables in a logic expression are replaced by their inverses, the AND operation is replaced by OR, the OR operation is replaced by AND, and the entire expression is inverted, the resulting logic expression yields the same values as before ELECTRICAL the changes. ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits NAND, NOR, and XOR Gates ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Sum-of-Products Implementation Product terms that include all of the input variables (or their inverses) are called minterms. In a sum-of-products expression, we form a product of all the input variables (or their inverses) for each row of the truth table for which the result is logic 1. The output is the sum ELECTRICAL ENGINEERING of these products. Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Product-of-Sums Implementation Sum terms that include all of the input variables (or their inverses) are called maxterms. In a product-of-sums expression, we form a sum of all the input variables (or their inverses) for each row of the truth table for which the result is logic 0. The output is the product of ELECTRICAL ENGINEERING these sums. Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Many useful combinatorial circuits known as decoders, encoders, or translators are available as integrated circuits. ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Karnaugh Maps ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits Sequential Circuits Outputs depend on PAST as well as PRESENT inputs Simple Memory Often synchronized by a “Clock” ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits ELECTRICAL ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 7 Logic Circuits
