Objectives, And or operation, Not operation, Fundamentals laws, Characteristic of logic families, Bipolar families, Diode logic, Resistor, transistor logic.

1. UNIT2
LOGIC GATES AND CIRCUITS

2. 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.

3. 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.
• 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.
• John Atanasoff and Claude Shannon were among the first to see this connection.

4. • In the middle of the twentieth century, computers were commonly known as “thinking
machines” and “electronic brains.”
• 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.
• Many people, however, are still fearful of them.
• In this chapter, you will learn the simplicity that constitutes the essence of the machine.

5. BOOLEAN ALGEBRA
• Boolean algebra is a mathematical system for the manipulation of variables that can have
one of two values.
• In formal logic, these values are “true” and “false.”
• 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.
• Common Boolean operators include AND, OR, and NOT.

6. AND, OR OPERATION
• 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.

7. NOT OPERATION
• 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. FUNDAMENTAL LAWS
•Associative laws
•(A + B)+ C = A+ (B + C)
•(AB)C = A (BC)
• Distributive laws
•A (B + C) = AB + AC

9. •Related identities
•(A + AB)= A
•(A + B)= A+ B
•(A+B)• (A+C) =(A+BC)
•Commutative Law
•A + B = B + A

10. • It implies that the input A and B of the OR gate can be interchanged without changing
the output Y. It can be justified from the truth table of two-input OR gate. For A = B, it
is obvious that it doesn’t matter when we interchange A and B. When A = 0 and B = 1, if
we interchange A and B, then it will become the case of A = 1 and B = 0 and for both
these case the output is 1. Hence it doesn’t matter to the output if we interchange A and B
inputs.
• Associative Law
• A + B + C = (A + B) + C = A + (B + C)

11. BOOLEAN FUNCTION
• 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}.

12. • The truth table for the Boolean function:
F(X,Y,Z)=X 𝑧+Y
is shown at the right.
• To make evaluation of the Boolean function easier, the truth
table contains extra (shaded) columns to hold evaluations of
subparts of the function.

13. • As with common arithmetic, Boolean operations have rules of
precedence.
• The NOT operator has highest priority, followed by AND and
then OR.
• This is how we chose the (shaded) function subparts in our
table.

14. • Digital computers contain circuits that implement Boolean functions.
• The simpler that we can make a Boolean function, the smaller the circuit that will result.
• Simpler circuits are cheaper to build, consume less power, and run faster than
complex circuits.
• With this in mind, we always want to reduce our Boolean functions to their simplest form.
• There are a number of Boolean identities that help us to do this.

15. DE MORGAN'S THEOREM
• Sometimes it is more economical to build a circuit using the complement of a function
(and complementing its result) than it is to implement the function directly.
• DeMorgan’s law provides an easy way of finding the complement of a Boolean function.
• Recall DeMorgan’s law states:
• 𝑥𝑦 = 𝑥 + 𝑦 and 𝑥 + 𝑦 = 𝑥 𝑦

16. • DeMorgan’s law can be extended to any number of variables.
• Replace each variable by its complement and change all ANDs to ORs and all ORs to
ANDs.
• Thus, we find the the complement of:
𝐹 𝑋, 𝑌, 𝑍 = (𝑋𝑌)+( 𝑥𝑍) + 𝑌 𝑧)
𝐹 𝑋, 𝑌, 𝑍 = 𝑥𝑦 + 𝑥𝑧 + 𝑦 𝑧
= 𝑥𝑦 𝑥𝑧 𝑦 𝑧
= 𝑥 + 𝑦 𝑥 + 𝑍 𝑦 + 𝑧

17. LOGIC GATES
• The three simplest gates are the AND, OR, and NOT gates.
• They correspond directly to their respective Boolean operations, as you can see by their
truth tables.

18. • Another very useful gate is the exclusive OR (XOR) gate.
• The output of the XOR operation is true only when the values of the inputs differ.

19. • NAND and NOR are two very important gates. Their symbols and truth tables are
shown at the right.

20. • NAND and NOR are known as universal gates because they are inexpensive to
manufacture and any Boolean function can be constructed using only NAND or only
NOR gates.

21. • Gates can have multiple inputs and more than one output.
• A second output can be provided for the complement of the operation.
• We’ll see more of this later.

22. CHARACTERISTICS OF LOGIC FAMILIES
• The main characteristics of logic families include:
• Speed
• Fan-in
• Fan-our
• Noise immunity
• Power dissipation

23. • Speed:speed of a logic circuits is determined by the time between the application of input
and change in the output of the circuits.
• Fan-in:It determines the number of inputs the logic gate can handle.
• Fan-out:Determines the number of circuits that a gate can drive.
• Noisy immunity:Maximum noise that a circuit can withstand without affecting the output.
• Power:When a circuit switches from one state to other ,power dissipates.

24. BIPOLAR FAMILIES
• Bipolar transistors are fabricated on a chip in digital integrated circuits.
• Bipolar technology is preferred for SSI[Small scale integrated]and MS[Medium scale
integration]because it is faster.
• TYPES OF BIPOLAR FAMILIES:
• Diode Logic(DL)
• Register Transistor Logic(RTL)
• Diode Transistor Logic
• Transistor-Transistor Logic

25. DIODE LOGIC
In DDL(diode logic),only Diode and Resistors are used for implementing a particular
logic.Remember that the Diode conducts only when it is Forward Biased.

26. • DISADVANTAGES OF DIODE LOGIC:
• Diode Logic suffers from voltage degradation from one stage to the next.
• Diode Logic only permits OR and AND functions.

27. RESISTOR TRANSISTOR LOGIC
• In RTL(resistor transistor logic),all the logic are implemented using resistors and
transistors.one basic thing about the transistor(NPN),is the HIGH at input causes output to
be LOW (i.e.like a inverter).in the case of PNP transistor,the LOW at input causes ouput
to be HIGH.

28. • ADVANTAGE:
• Less number of transistors
• DISADVANTAGES:
• High power dissipation
• Low fan in

29. DIODE TRANSISTOR LOGIC
• In DTL(Diode transistor logic),all the logic is implemented using diodes and transistors.
• DISADVANTAGE:
• Propogation delay is larger

30. TRANSISTOR TRANSISTOR LOGIC
• The first transistor-transistor logic family of integrated circuits was introduced by
Sylvania as Sylvania universal high-level logic(SUHL)in 1963 Texas instruments
introduced 7400 series TTL family in 1964.
• Transistor –transistor logic uses bipolar transistor to form its integrated circuits.
• TTL has changed significantly over the years,with newer versions replacing the old types.

32. INTEGRATED CIRCUITS
• When integrated circuits are used,one or more complete gates or other circuits are
packaged in a single integrated –circuits(IC)container.
• The IC containers provide input and output pins or connections,which or then
interconnected by plated strips on circuit boards,wires,or other means.to form complete
computing devices.
• There are two basic techniques for manufacturing ICs-bipolar and metal-oxide
semiconductor(MOS).

33. THANK YOU