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ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Chapter 7Logic 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, andother forms.
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic 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
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic 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
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
DefinitionsPositive 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
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Binary Numbers
101210 1021031041072.743 −×+×+×+×=
1010123
2 5.1321212021271.1101 =×+×+×+×+×= −
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Gray Code
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Complement Arithmetic
The one’s complement of a binary number is obtained by replacing 1s by 0s, and vice versa.
0100110110110010 (one’s complement)
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic 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
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Subtraction Using Two’s-Complement Arithmetic
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
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
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
AAA =
AA =1
00 =ABAAB =
( ) ( ) ABCCABBCA ==
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
0=AA
AA =
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
( ) ( ) CBACBACBA ++=++=++
( ) ACABCBA +=+
AA =+ 0
11 =+A
1=+ AA
AAA =+
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Boolean algebra expressions can be implemented by interconnection of AND gates, OR gates, and inverters.
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
De Morgan’s Laws
CBAABC ++= ( ) FEDFED =++
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
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
NAND, NOR, and XOR Gates
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic 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 of these products.
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic 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 these sums.
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Many useful combinatorial circuits known as decoders, encoders, or translators are available as integrated circuits.
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Karnaugh Maps
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
Sequential Circuits
Outputs depend on PAST as well as PRESENT inputs
Simple Memory
Often synchronized by a “Clock”
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
ELECTRICAL
ENGINEERINGPrinciples and
Applications
SE OND EDITION
Chapter 7Logic Circuits
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