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Chapter 1 Introduction
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What is a Computer? Electronic device that takes in data and instructions (input), works with the data (processing) and Put out the information (output)
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Computer Components Hardware Software Input devices CPU
Storage devices Output devices Software System software Programs
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Generations of Computers
First generation vacuum tube-based electronic computer. Use machine language. Very large and slow.
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Generations of Computers
second generation transistor-based electronic computer. Reduction in size and cost. More faster Use assembly language.
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Generations of Computers
Third generation integrated circuits replaced several individually wired transistors. Faster and smaller in size. Use programming languages such as: C Fortran Basic Cobol
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Generations of Computers
Forth generation Use large-scale integration technology. the need to speed up the software development process Use friendly programming languages.
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Generations of Computers
Fifth generation Very Large-Scale Integration technology (VLSI).. make use of parallel processing Artificial intelligence Prolog
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Range of Computers Embedded Systems chips in washing machines,
laser printers hand calculators.
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Range of Computers Microcomputers personal computers Multitasking
Networking PRICE: between $700 - $2000
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Range of Computers Minicomputers
These perform multi-tasking and allow many terminals to be connected to their services. Business, to process large amount of data. PRICE: between $15,000 - $150,000
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Mainframe Computers Mainframe computers are large general purpose
Large databases. government departments and the airline industry
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Supercomputers very fast and have multiple processors.
developed for scientific applications usually involving complex arithmetic and mathematical operations.
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Basic Computer System ALU Control Unit Registers internal bus.
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Fetch and Execute
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Input devices Keyboard Mouse Joystick Light pin ……
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Introduction to Digital Concepts
Chapter 2 Introduction to Digital Concepts
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Analog Representation
Voltage, current, movement
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Digital Representation
Digital watch
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Advantages of Digital Techniques
Easer to design. (processing limited values). Information storage is easy. More accuracy. Operation can be programmed. Less affected by noise.
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Limitations of Digital Techniques
The real world is mainly analog need to be converted to digital (ADC) Process the digtal form Convert the digital output to analog (DAC).
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Example
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Digital Number System
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Representing Binary Quantites
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Digital Waveform
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Pulse Types Periodic Pulse repeat itself at fixed intervals.
A frequency is the rate at which the waveform repeats
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Pulse Types
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Pulse Types Non periodic pulse
Does not repeat itself at fixed intervals.
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Example
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A Digital Waveform Carries Binary Information.
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Timing Diagram Showing the relationship of all waveforms
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Data Transfer Serial Form
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Data Transfer Parallel form
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Number System and Codes
Chapter 3 Number System and Codes
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Decimal and Binary Numbers
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Decimal and Binary Numbers
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Converting Decimal to Binary
Sum of powers of 2
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Converting Decimal to Binary
Repeated Division
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Binary Numbers and Computers
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Hexadecimal Numbers
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Converting decimal to hexadecimal
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Converting binary to hexadecimal
Converting hexadecimal to binary?
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Hexadecimal numbers
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Binary arithmetic Binary addition
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Representing Integers with binary
Some of challenges:- Integers can be positive or negative Each integer should have a unique representation The addition and subtraction should be efficient.
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Representing a positive numbers
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Representing a negative numbers using Sign-Magnitude notation
-5 = bits sign-manitude -55= bits sign-magnitude
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1’s Complement The 1’s complement representation of the positive number is the same as sign-magnitude. +84 =
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1’s Complement The 1’s complement representation of the negative number uses the following rule:- Subtract the magnitude from 2n-1 For example: -36 = ??? +36 =
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1’s Complement Example :- - 57 +57 = -57 =
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Converting to decimal format
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2’s Complement For negative numbers:-
Subtract the magnitude from 2n. Or Add 1 to the 1’s complement
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Example
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Convert to decimal value
Positive values:- = +89 Negative values
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Two's Complement Arithmetic
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Adding Positive Integers in 2's Complement Form
Overflow in Binary Addition
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Overflow in Binary Addition
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Overflow in Binary Addition
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Overflow in Binary Addition
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Adding Positive and Negative Integers in 2's Complement Form
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Adding Positive and Negative Integers in 2's Complement Form
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Subtraction of Positive and Negative Integers
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Digital Codes Binary Coded Decimal (BCD)
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BCD
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BCD
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4221 Code
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Gray Code In pure binary coding or 8421 BCD then counting from 7 (0111) to 8 (1000) requires 4 bits to be changed simultaneously. Gray coding avoids this since only one bit changes between subsequent numbers
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Binary –to-Gray Code Conversion
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Gray –to-Binary Conversion
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Gray –to-Binary Conversion
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The Excess-3- Code
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Parity The method of parity is widely used as a method of error detection. Extar bit known as parity is added to data word The new data word is then transmitted. Two systems are used: Even parity: the number of 1’s must be even. Odd parity: the number of 1’s must be odd.
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Parity Example: Odd parity Even Parity 110010 110011 11001 111101
111100 11110 110001 110000 11000
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Logic Gates and Boolean Algebra
Chapter 4 Logic Gates and Boolean Algebra
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Introduction Logic gates are the actual physical implementations of the logical operators. These gates form the basic building blocks for all digital logic circuits. Logic gates process signals which represent true or false.
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Switch S1 AND Switch S2 must be closed to light the lamp
Introduction Gates are identified by their function: NOT, AND, NAND, OR, NOR, EX-OR and EX-NOR. Switch S1 AND Switch S2 must be closed to light the lamp Switch S1 OR Switch S2 (or both of them) must be closed to light the lamp
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Truth Table A truth table is a means for describing how a logic circuit's output depends on the logic levels present at the circuit's inputs.
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Logic Gates and Circuit Diagrams
OR Gate
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Logic Gates and Circuit Diagrams
AND Gate
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Logic Gates and Circuit Diagrams
NOT Gate
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Logic Gates and Circuit Diagrams
NOR Gate
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Logic Gates and Circuit Diagrams
NAND Gate
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Logic Gates and Circuit Diagrams
EX-OR gate The 'Exclusive-OR' gate is a circuit which will give a high output if either but not both, of its two inputs are high. EX-NOR gate is The inversion of EX-OR Gate
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Describing Logic Circuits Algebraically
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Describing Logic Circuits Algebraically
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Evaluating Logic Circuit Outputs
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Evaluating Logic Circuit Outputs
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Determining Output Level from a Diagram
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Implementing Circuits From Boolean Expression
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Boolean Algebra Simplification of logical circuits.
One tool to reduce logical expressions is the mathematics of logical expressions. The rules of Boolean Algebra are simple and straight-forward, and can be applied to any logical expression.
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Boolean Algebra
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Boolean Algebra
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Boolean Algebra (A’B)’(A+B) Solution: (A + B’) (A + B)
AA + B’A + AB + B’B A + B’A + AB A + AB A AB(A + B’C +C) Solution: ABA + ABB’C + ABC AB ABC AB + ABC AB
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Boolean Algebra
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Universality of NAND & NOR Gates
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Universality of NAND & NOR Gates
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Alternate Logic Gate Representations
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Forms and Definitions of Boolean Expressions
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Product of Sums Representation
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Disjunctive Normal Form
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Disjunctive Normal Form
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Disjunctive Normal Form
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Disjunctive Normal Form
Using truth tables, convert this expression into a sum of minterms
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Flowcharts and programming Techniques
Chapter 5 Flowcharts and programming Techniques
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Introduction A flowchart is a diagram consisting of labeled geometrical symbols together with rows connecting one symbol to another A program flowchart pictures the sequence of instructions for solving a particular problem ( usually by means of a computer program).
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Introduction BOUNS = 0.03 * SALARY
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Introduction The sequence of instructions for solving a particular problem is called algorithm. Express the algorithm through a flowchart Easier to draw the flowchart than to write the program directly. Easier to understand than program Easy for development. Flowcharts are independent of any particular programming language
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VARIABLES ,DATA-NAMES, PROGRAMMING SATATEMENTS
a variable means a data item whose value may change during the execution of the program. Examples:- Salary Bouns AVERAGE Assignment Statements Salary = 500 Bouns = 0,03*Salary AVERAGE = ( T1+T2+T3)/3
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VARIABLES ,DATA-NAMES, PROGRAMMING SATATEMENTS
HOURS = HOURS + 12 Counter = Counter + 1
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Input/Output Statements
Read NUMBER, HOURS,RATE Write NUMBER, GROSS , NET
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FLOWCHART SYMBLOS
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FLOWCHART SYMBLOS Terminal symbol Input/Output symbol
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FLOWCHART SYMBLOS process symbol
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FLOWCHART SYMBLOS Decision symbol.
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FLOWCHART SYMBLOS Example: A company plans to give a year-end 3% to each of its employees. However, if an employee has been working 10 or more years at the company , he is to get an additional $50.
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FLOWCHART SYMBLOS
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FLOWCHART SYMBLOS Example: The HP company plans to give a year-end 3% bonus to each of its employees earning $10,000 or more per year , and a fixed $300 bonus for the other employees.
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FLOWCHART SYMBLOS
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LOOPS AND THEIR CONTROL BY A COUNTER
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LOOPS AND THEIR CONTROL BY A COUNTER
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CONTROL OF LOOPS BY HEADER OF TRALIER RECORDS
Control by a Header Record
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CONTROL OF LOOPS BY HEADER OF TRALIER RECORDS
Control by a Trailer Record
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ACCUMULATORS
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ACCUMULATORS Example : Suppose that a company wants to find the total salary paid to its employees of a company.
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TWO SPECIAL ALGORITHMS:
The average of the salaries,
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TWO SPECIAL ALGORITHMS:
The largest salary
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DO LOOPS
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DO LOOPS Example: A company has 80 employees . Draw a flowchart to find the average salary and the number of employees earning above the average salary
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Example
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