ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc. Chapter 7 Logic Circuits

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc. 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, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc. 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. 8. Understand how gates are connected together to form flip-flops and registers.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

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, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc. 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, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc. Binary Numbers

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

Gray Code

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

Complement Arithmetic The one’s complement of a binary number is obtained by replacing 1s by 0s, and vice versa (one’s complement)

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc. 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, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc. Subtraction Using Two’s- Complement Arithmetic

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc. Overflow and Underflow In performing arithmetic using two’s- complement 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, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

Boolean algebra expressions can be implemented by interconnection of AND gates, OR gates, and inverters.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

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 the changes.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

NAND, NOR, and XOR Gates

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

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 of these products.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

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 these sums.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

Many useful combinatorial circuits known as decoders, encoders, or translators are available as integrated circuits.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.

Karnaugh Maps

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.