This document discusses digital logic design and covers the following topics:
- It outlines the course grading breakdown of a digital logic design course.
- It introduces basic logic gates like AND, OR, NOT and describes how they are combined to build half adders and full adders.
- It explains logic gates in detail including Boolean expressions, truth tables and logic diagrams. Transistors are described as the basic building blocks of computers that are combined to implement logic functions.
FYBSC IT Digital Electronics Unit II Chapter I Boolean Algebra and Logic GatesArti Parab Academics
Boolean Algebra and Logic Gates:
Introduction, Logic (AND OR NOT), Boolean theorems, Boolean
Laws, De Morgan’s Theorem, Perfect Induction, Reduction of Logic
expression using Boolean Algebra, Deriving Boolean expression from
given circuit, exclusive OR and Exclusive NOR gates, Universal Logic
gates, Implementation of other gates using universal gates, Input
bubbled logic, Assertion level.
FYBSC IT Digital Electronics Unit II Chapter I Boolean Algebra and Logic GatesArti Parab Academics
Boolean Algebra and Logic Gates:
Introduction, Logic (AND OR NOT), Boolean theorems, Boolean
Laws, De Morgan’s Theorem, Perfect Induction, Reduction of Logic
expression using Boolean Algebra, Deriving Boolean expression from
given circuit, exclusive OR and Exclusive NOR gates, Universal Logic
gates, Implementation of other gates using universal gates, Input
bubbled logic, Assertion level.
M. FLORENCE DAYANA/unit - II logic gates and circuits.pdfDr.Florence Dayana
Logic Gates, Truth Table, AND Gate
Types of Digital Logic AND Gate, The 2-input and 3-input AND Gate, OR Gate, Types of Digital Logic AND Gate, The 2-input OR gate, The 3-input OR gate, NOT Gate, NAND Gate, The 2-input NAND Gate, The 3-input NAND Gate, NOR Gate, 2-input NOR gate
Just like other gates, XOR gate or Exclusive-OR gate
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2. Grading
LFU 20142
Course Grading:
Midterm Exam 25%
Course Work and Assignments 15%
Final Exam 60%
Total 100%
3. What does this chapter give you?
LFU 20143
Identify the basic gates and describe the behavior of
each.
Describe the behavior of a gate or circuit using
Boolean expressions, truth tables, and logic
diagrams.
Combine basic gates into circuits.
How to build half adder
and a full adder.
5. Introduction
LFU 20145
Boolean functions may be practically implemented by
using electronic gates. The following points are
important to understand:
1- Electronic gates require a power supply.
2- Gate INPUTS are driven by voltages having two
nominal values, e.g. 0V and 5V representing logic 0
and logic 1 respectively.
6. Introduction
LFU 20146
3- The OUTPUT of a gate provides two nominal values
of voltage only, e.g. 0V and 5V representing logic 0
and logic 1 respectively. In general, there is only one
output to a logic gate except in some special cases.
4- There is always a time delay between an input
being applied and the output responding.
7. Introduction
Transistor Building Block of Computers
Microprocessors contain millions of transistors
Intel Pentium 4 (2000): 48 million
IBM PowerPC 750FX (2002): 38 million
IBM/Apple PowerPC G5 (2003): 58 million
Logically, each transistor acts as a switch
Combined to implement logic functions
AND, OR, NOT
Combined to build higher-level structures
Adder, multiplexer, decoder, register, …
8. Logic Gates – Binary Logic
LFU 20148
Binary variables take one of two values.
Logical operators operate on binary values and
binary variables.
Basic logical operators are the logic functions AND,
OR and NOT.
Logic gates implement logic functions.
Boolean Algebra: a useful mathematical system for
specifying and transforming logic functions.
We study Boolean algebra as a foundation for
designing and analyzing digital systems!
9. Logic Gates – Binary Variables
LFU 20149
Remember that the two binary values have different
names:
True/False
On/Off
Yes/No
1/0
We use 1 and 0 to denote the two values.
Variable identifier examples:
A, B, y, z
10. Logic Gates – Logical operations
LFU 201410
The three basic logical operations are:
AND
OR
NOT
AND is denoted by a dot (·).
OR is denoted by a plus (+).
NOT is denoted by an overbar ( ¯ ), a single quote
mark (') after, or (~) before the variable.
11. Logic Gates – Notation Examples
LFU 201411
Examples:
is read “Y is equal to A AND B.”
is read “z is equal to x OR y.”
is read “X is equal to NOT A.”
Note: The statement:
1 + 1 = 2 (read “one plus one equals two”)
is not the same as
1 + 1 = 1 (read “1 or 1 equals 1”).
= BAY
yxz +=
AX =
12. Logic Gates
LFU 201412
A Logical gate is a device that performs a basic
operation on electrical signals, and these gates are
combined into circuits to perform more complicated
tasks.
All basic logic gates have the ability to accept either
one or two input signals (depending upon the type of
gate) and generate one output signal.
13. Logic Gates Representation
LFU 201413
There are three different methods for describing the
behavior of gates and circuits:
Boolean expressions
Logic diagrams
Truth tables
14. Logic Gates Representation
LFU 201414
Boolean expressions: expressions in this algebraic
notation are an smart way to show the activity of
electrical circuits.
Logic diagrams: a graphical representation of a
circuit and each type of gate is represented by a
specific graphical symbol
Truth tables: defines the function of a gate by listing
all possible input combinations that the gate could
encounter, and the corresponding output
15. Logic Gates
LFU 201415
Let’s take the processing of the following six types of
gates:
NOT
AND
OR
NAND
NOR
XOR
16. NOT Gate
LFU 201416
A NOT gate accepts only one input value
and produces one output value
By definition, if the input value for a NOT gate is 0,
the output value is 1, and if the input value is 1, the
output is 0
A NOT gate is sometimes called as an inverter
because it inverts the input value
17. AND Gate
LFU 201417
An AND gate accepts two input signals.
If the two input values for an AND gate are both 1,
the output is 1; otherwise, the output is 0
18. OR Gate
LFU 201418
An OR gate accepts two input signals.
If the two input values are both 0, the output value is
0; otherwise, the output is 1
19. XOR , or exclusive OR Gate
LFU 201419
An XOR gate produces 0 if its two inputs are the
same, and a 1 otherwise.
Note the difference between the XOR gate
and the OR gate; they differ only in one
input situation, when both input signals are 1, the OR
gate produces a 1 and the XOR produces a 0
20. NAND and NOR Gates
LFU 201420
The NAND and NOR gates are basically the
opposite of the AND and OR gates, respectively:
NAND gate:
NOR gate:
21. Review of Logic Gates
LFU 201421
A NOT gate inverts its single input value .
An AND gate produces 1 if both input values are 1 .
An OR gate produces 1 if one or the other or both input
values are 1 .
An XOR gate produces 1 if one or the other (but not both)
input values are 1 .
A NAND gate produces the opposite results of an AND
gate .
A NOR gate produces the opposite results of an OR gate
.
23. Half Adder
LFU 201423
Half adder is a combinational logic circuit with two
input and two output. The half adder circuit is
designed to add two single bit binary number A and
B. It is the basic building block for addition of two
single bit numbers. This circuit has two
outputs carry and sum.
25. Full Adder
LFU 201425
Full adder is developed to overcome the drawback of
Half Adder circuit. It can add two one-bit numbers A
and B, and carry c. The full adder is a three input
and two output combinational circuit.
28. End of Chapter 3
LFU 201428
Note : The PowerPoint slides are taken from internet websites and a
variety of presentations.
All the basic logic gates