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Digital Logic DesignIT101LGD

Prepared By

Asst. Lect. Mohammed Salim

Department of IT

Chapter 3 Logic Gates

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LFU_IT_Logic

Design

Grading

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Course Grading:

Midterm Exam 25%Course Work and Assignments 15%Final Exam 60%Total 100%

What does this chapter give you?

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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.

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Contents

Introduction

Logic Gates

Half-Adder

Full-Adder

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Introduction

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.

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Introduction

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.

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, …

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Logic Gates – Binary Logic 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!

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Logic Gates – Binary Variables 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

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Logic Gates – Logical operations 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.

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Logic Gates – Notation Examples

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 =

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Logic Gates 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.

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Logic Gates Representation There are three different methods for

describing the behavior of gates and circuits:

Boolean expressions

Logic diagrams

Truth tables

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Logic Gates Representation 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

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Logic Gates Let’s take the processing of the following six

types of gates:

NOT AND OR NAND NOR XOR

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NOT Gate 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

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AND Gate 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

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OR Gate 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

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XOR , or exclusive OR Gate 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

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NAND and NOR Gates

The NAND and NOR gates are basically the opposite of the AND and OR gates, respectively:

NAND gate:

NOR gate:

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Review of Logic Gates 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 .

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Logic Gates Processor Example

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Half Adder 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.

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Half Adder

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Full Adder 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.

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Full Adder

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Full Adder

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End of Chapter 3 Note : The PowerPoint slides are taken from internet websites

and a variety of presentations.All the basic logic gates