aim repaired) repaired)

Download AIM Repaired) Repaired)

Post on 05-Apr-2018

217 views

Category:

Documents

0 download

Embed Size (px)

TRANSCRIPT

  • 7/31/2019 AIM Repaired) Repaired)

    1/14

    ECE

    PREPARED BY,

    LAVANYA. M

    ECE

    DIGITAL PRINCIPLES AND

    SYSTEM DESIGN

  • 7/31/2019 AIM Repaired) Repaired)

    2/14

    AIM:

    To provide an in-depth knowledge of the design of digital circuits and the use of Hardware

    Description Language in digital system design.

    OBJECTIVES :

    To understand different methods used for the simplification of Boolean functions To design and implement combinational circuits To design and implement synchronous

    sequential circuits

    To design and implement asynchronous sequential circuits To study the fundamentals ofVHDL / Verilog HDL

    UNIT I BOOLEAN ALGEBRA AND LOGIC GATES

    Review of binary number systems - Binary arithmetic Binary codes Boolean algebra andtheorems - Boolean functions Simplifications of Boolean functions using Karnaugh map and

    tabulation methods Implementation of Boolean functions using logic gates

    UNIT II COMBINATIONAL LOGIC

    Combinational circuits Analysis and design procedures - Circuits for arithmetic operations -

    Code conversion Introduction to Hardware Description Language (HDL)

    UNIT III DESIGN WITH MSI DEVICES

    Decoders and encoders - Multiplexers and demultiplexers - Memory and programmable logic -HDL for combinational circuits

    UNIT IV SYNCHRONOUS SEQUENTIAL LOGIC

    Sequential circuits Flip flops Analysis and design procedures - State reduction and state

    assignment - Shift registers Counters HDL for Sequential Circuits.

    UNIT V ASYNCHRONOUS SEQUENTIAL LOGIC Analysis and design of asynchronous

    sequential circuits - Reduction of state and flow tables Race-free state assignment Hazards,

    ASM Chart.

    TEXT BOOKS

    1. M.Morris Mano, Digital Design, 3rd edition, Pearson Education, 2007.REFERENCES 1.

    Charles H.Roth, Jr. Fundamentals of Logic Design, 4th Edition, Jaico Publishing House,

    Cengage Earning, 5th ed, 2005. 2. Donald D.Givone, Digital Principles and Design, Tata

    McGraw-Hill, 2007

  • 7/31/2019 AIM Repaired) Repaired)

    3/14

    BOOLEAN ALGEBRA AND LOGIC GATES

    INTRODUCTION:

    OBJECTIVES :

    To understand basic number systems and complements, and also number systemconversion.

    Review of binary number systems:

    The term digital refers to any process that is accomplished using discrete units Digital computer is the best example of a digital system.

    Basically deal with two types of signals in electronics

    i) Analog

    ii) Digital

  • 7/31/2019 AIM Repaired) Repaired)

    4/14

    Types of Number Systems are

    i) Decimal Number system

    ii) Binary Number system

    iii) Octal Number system

    iv) Hexadecimal Number system

    Complements :

    Complements are used in digital computers for simplifying the subtraction operation and for

    logical manipulation. There are two types of complements

    i) rs complement

    ii) (r-1)s complement.

  • 7/31/2019 AIM Repaired) Repaired)

    5/14

    NUMBER SYSTEM FORMAT:

    Dec Hex Oct Bin0

    1

    23

    4

    56

    7

    89

    10

    11

    12

    1314

    15

    0

    1

    23

    4

    56

    7

    89

    A

    B

    C

    DE

    F

    000

    001

    002003

    004

    005006

    007

    010011

    012

    013

    014

    015016

    017

    00000000

    00000001

    0000001000000011

    00000100

    0000010100000110

    00000111

    0000100000001001

    00001010

    00001011

    00001100

    0000110100001110

    00001111

    Binary to decimal conversion:

    Step1: Assigning position to Binary number

    Step 2:Draw lines, starting from the right, connecting each consecutive digit of the binary

    number to the power of two that is next in the list above it.

  • 7/31/2019 AIM Repaired) Repaired)

    6/14

    Step 3:Move through each digit of the binary number. If the digit is a 1, write its

    corresponding power of two below the line, under the digit. If the digit is a 0, write a 0 below theline, under the digit.

    Step4:

    Add the numbers written below the line. The sum should be 155. This is the decimal

    equivalent of the binary number 10011011. Or, written with base subscripts:

    Step5:Repetition of this method will result in memorization of the powers of two, whichwill allow you to skip step 1.

    Binary to octal(vive versa):

    Every octal digit can be re-written as three binary bits and vice versa.octal binary octal binary

    octal binary octal binary

    0 0 = 022+0210 000 4 4 = 122+0210100

  • 7/31/2019 AIM Repaired) Repaired)

    7/14

    1 1 = 022+0211 001 5 5 = 122+0211 101

    2 2 = 022+1210 010 6 6 = 122+1210 110

    3 3 = 022+1211 011 7 7 = 122+1211 111

    Example: Convert375 (octal) to binary

    3/7/5 =011/111/101 binary

    Example: Convert 10110100 (binary) to octal

    10 /110/100= 264octal

    Hexadecimal to octal conversion

    Hexadecimal to octal conversion proceeds by first converting the hexadecimal digits to 4-bit

    binary values, then regrouping the binary bits into 3-bit octal digits.

    For example, to convert 3FA516:

    To binary:

    3 F A 5

    0011 1111 1010 0101

    then to octal:

    0 011 111 110 100 101

    0 3 7 6 4 5

    Therefore, 3FA516 = 376458.

    Octal to hexadecimal conversion

    The conversion is made in two steps using binary as an intermediate base. Octal is converted to

    binary and then binary to hexadecimal, grouping digits by fours, which correspond each to a

    hexadecimal digit.

    For instance, convert octal 1057 to hexadecimal:

    To binary:

    1 0 5 7

    001 000 101 111

    then to hexadecimal:

    0010 0010 1111

  • 7/31/2019 AIM Repaired) Repaired)

    8/14

    2 2 F

    Therefore, 10578 = 22F16.

    Binary to octal conversion

    The process is the reverse of the previous algorithm. The binary digits are grouped by threes,

    starting from the decimal point and proceeding to the left and to the right. Add leading 0s (ortrailing zeros to the right of decimal point) to fill out the last group of three if necessary. Then

    replace each trio with the equivalent octal digit.

    For instance, convert binary 1010111100 to octal:

    001 010 111 100

    1 2 7 4

    Therefore, 10101111002 = 12748.

    Convert binary 11100.01001 to octal:

    011 100 . 010 010

    3 4 . 2 2

    Therefore, 11100.010012 = 34.22

    Octal to decimal conversion

    To convert a number kto decimal, use the formula that defines its base-8 representation:

    In this formula, ai is an individual octal digit being converted, where i is the position of the digit

    (counting from 0 for the right-most digit).

    Example: Convert 7648 to decimal:

    7648 = 782 + 681 + 480 = 448 + 48 + 4 = 50010

  • 7/31/2019 AIM Repaired) Repaired)

    9/14

    For double-digit octal numbers this method amounts to multiplying the lead digit by 8 and

    adding the second digit to get the total.

    Example: 658 = 68 + 5 = 5310Binary to hexadecimal conversion:

    Conversion between hex and binary is easy. Simply substitute four-bit groups for the hex digit of

    the same value. Specifically:

    Hex Digit: 0 1 2 3 4 5 6 7

    Bit Group: 0000 0001 0010 0011 0100 0101 0110 0111

    Hex Digit: 8 9 a b c d e f

    Bit Group: 1000 1001 1010 1011 1100 1101 1110 1111

    For conversion from hex to binary, simply string together the bits for each hex digit. For

    instance, 0x509d7a is binary 10100001001110101111010. To wit:

    Hex Number: 5 0 9 d 7 a

    Binary Number: 0101 0000 1001 1101 0111 1010

    To convert the other way, break the binary number into groups of four, then replace each one

    with its hex digit. Group the digits starting from the right. If you don't have a complete group of

    four when you reach the left,pad with zero bits on the leftto fill the last group. For instance,

    binary 111011011111110001 is 0x3b7f1:

    Binary Groups: 0011 1011 0111 1111 0001

    Hex Digits: 3 b 7 f 1

    Because this conversion is so easy, the easiest way to convert between binary and decimal isusually to go through hex. It generally requires fewer operations,

    Questions:

    1.What is meant by radix?

    2. What is the base of hexadecimal?

    3.What is the use of Number syatem?

  • 7/31/2019 AIM Repaired) Repaired)

    10/14

    Boolean Algebra and Theorems

    Objective:

    To know about Boolean Basics and its uses in number system.

    Boolean algebra is a deductive mathematical system closed over the values zero andone (false and true).

    A binary operator defined over this set of values accepts a pair of boolean inputs andproduces a single boolean value. For example, the boolean AND operatoraccepts two

    boolean inputs and produces a single boolean output (the logical AND ofthe two inputs).

    Postulates:

    For any given algebra system, there are some initial assumptions, orpostulates, thatthe system follows. You can deduce additional rules, theorems, and other properties of the

    system from this basic set of postulates

    Closure:

    The boolean system is closedwith respect to a binary operator if for everypair of boolean values, it produces a boolean result. For example, logical AND is

    closed in the boolean system because it accepts only boolean operands and produces

    only boolean results.

  • 7/31/2019 AIM Repaired) Repaired)

    11/14

    LAWS AND THEOREMS OF BOOLEAN ALGEBRA

    Identity Dual

    Operations with 0 and 1:1. X + 0 = X (identity)

    3. X + 1 = 1 (null element)

    2. X.1 = X4. X.0 = 0