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CPS-304 DIGITAL LOGIC & DESIGN. Instructor : Ms. Saba Iqbal. Textbook Digital Design by Morris Mano , 2 nd Edition/ 3rd Edition/Digital Fundamentals. What’s Course About?. Introduction to concepts of digital logic, gates, and the digital circuits

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cps 304 digital logic design

CPS-304DIGITAL LOGIC & DESIGN

Instructor : Ms. Saba Iqbal

slide2

Textbook

    • Digital Design by Morris Mano , 2 nd Edition/ 3rd Edition/Digital Fundamentals.
what s course about
What’s Course About?
  • Introduction to concepts of digital logic, gates, and the digital circuits
  • Design and analysis of combinational and sequential circuits
  • Basics of logic design of computer hardware
course outline
Course Outline
  • Binary Systems
  • Binary Algebra
  • Simplification of Boolean Functions
  • Combinational Logic
  • Sequential Logic
  • MSI Sequential Circuits
digital systems
Digital Systems
  • Digital Computer follow a sequence of instructions, Digital System play a prominent role in this digital age
    • Communication, medical treatment, internet, DVD, CD, Space ,Programme.Scientific &Educational field ,ATC commercial etc.
    • called programs, that operate on given data
    • User can specify and change program or data according to needs
  • Like Digital Computers, most digital devices are programmable
  • Digital Systems have the ability to Manipulate discrete elements of information.
    • Any set that is restricted to a finite number of elements contains discrete information
      • 10 Decimal digits
      • 26 Alphabet letters
      • 52 Playing cards
      • 64 squares of a chessboard
digital systems1
Digital Systems
  • Digital Systems can do hundreds of millions of operations per second
  • Extreme reliability due to error-correcting codes
  • A Digital System is interconnection of digital modules
  • To understand Digital module, we need to know about digital circuits and their logical functions
  • Hardware Description Language (HDL) is a programming language that is suitable for describing digital circuit in a textual form
    • Simulate a digital system to verify operation before it is built
computer
COMPUTER

Analog Computer,. It responds to continuous signals.

Digital computer. It responds to 0 and 1. also called Binary.

Main Modules.

Memory Unit

Processor Unit

Control Unit

Input Device / Output Device

CPU Processor combined with Control Unit

Micro Processor. CPU in a Small integrated circuit

CPU combined with Memory and Interface control for i/p and o/p devices form a micro computer.

data flow
DATA FLOW
  • Fetch Time. Getting data and instructions from ALU and then issue command Fix time
  • Execute Time. ALU carries out execution Time is variable
  • Master clock. It is in control unit and control all functions
  • Memory
    • RAM Semi conductor memory & Ferrite core memory
    • Sequential Memory . Mag tape, mag disk, CD Floppy Mag Drum.
  • each info has a location and an address.
definations memory
DEFINATIONS MEMORY
  • Random Access Memory,. Access time to a location is constant.
  • Sequential access memory. Access time to all locations are different
  • Main memory and Secondary memory. How we store
    • Semi conductor Magnetic Material
    • Binary Req. as material can store only 1 and 0
  • Three things are stored, Instructions, Data, Address.
decimal number
Decimal Number
  • 7,392= 7x103 +3x102 + 9x101 + 2x100
    • Thousands, hundreds, etc…power of 10 implied by position of coefficient
  • Generally a decimal number is represented by a series of coefficients
    • a6 a5 a4 a3 a2 a1 a0.a-1 a-2 a-3 a-4
  • aj cofficient are any of the 10 digit (0,1,2…9)
  • Decimal number are base 10
binary number
Binary Number
  • Digital Systems manipulate discrete quantities of information in binary form
    • Operands in calculations
    • Decimal Digits
    • Results
  • Strings of binary digits (“bits”)
  • Two possible values 0 and 1
binary numbers
Binary Numbers
  • Each digit represents a power of 2
  • Coefficient have two possible values 0 and 1
  • Strings of binary digits (“bits”)
    • n bits can store numbers from 0 to 2n-1
    • n bits can store 2n distinct combinations of 1’s and 0’s
  • Each coefficient aj is multiplied by 2j
  • So 101 binary is

1 x 22 + 0 x21 + 1 x 20

or

1 x 4 + 0 x 2 + 1 x 1 = 5

bits bytes
BITs & Bytes
  • A bit (short for binary digit) is the smallest unit of data in a computer.
    • A bit can hold only one of two values: 0 or 1, corresponding to the electrical values of off or on, respectively.
    • Because bits are so small, you rarely work with information one bit at a time
    • A byte is a unit of measure for digital information.
    • A single byte contains eight consecutive bits
  • Binary Arithmetic. Addition, Subtraction Multiplication
  • Give example
octal
Octal
  • Octal is base 8
  • A number is represented by a series of coefficients
    • a6 a5 a4 a3 a2 a1 a0.a-1 a-2 a-3 a-4
  • aj cofficient are any of 8 digit (0,1,2…7)
  • Need 3 bits for representation
  • Example:

(127.4)8= 1 X 82 +2 X 81 +7 X 80 + 4 X 8-1

64+16+7+.5= (87.5)10

hexadecimal
Hexadecimal
  • Hexadecimal is base 16
  • A number is represented by a series of coefficients
    • a6 a5 a4 a3 a2 a1 a0.a-1 a-2 a-3 a-4
  • aj cofficient are any of 16 digit (0,1,2,3,4,5,6,7,8, 9,A,B,C,D,E,F)
  • Need 4 bits for representation
  • (B65F)16

11 X 163 +6 X 162 + 5 X 161 +15 X 160

= 11x4096 + 6x256 +5x16 +15

= 45056 + 1536 + 80 +15 = 46,687

converting binary to decimal
Converting Binary to Decimal
  • Easy, just multiply digit by power of 2
  • Just like a decimal number is represented
  • Example follows
binary decimal example
Binary  Decimal Example

What is 10011100 in decimal?

128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156

decimal to binary
Decimal to Binary
  • A little more work than binary to decimal
  • Some examples
    • 3 = 2 + 1 = 11 (that’s 1•21 + 1•20)
    • 5 = 4 + 1 = 101 (that’s 1•22 + 0•21 + 1•20)
algorithm decimal to binary
Algorithm – Decimal to Binary
  • Find largest power-of-two smaller than decimal number
  • Make the appropriate binary digit a ‘1’
  • Subtract the power of 2 from decimal
  • Do the same thing again
decimal binary example
Decimal  Binary Example
  • Convert 28 decimal to binary

32 is too large, so use 16

Binary  10000

Decimal  28 – 16 = 12

Next is 8

Binary  11000

Decimal  12 – 8 = 4

Next is 4

Binary  11100

Decimal  4 – 4 = 0

decimal binary fraction
Decimal  Binary (Fraction)
  • Convert decimal 0.6875 to binary

Integer Fraction Coefficient

0.6875 X 2= 1 0.3750 a-1=1

0.3750 X 2= 0 0.7500 a-2=0

0.7500 X 2= 1 0.5000 a-3=1

0.5000 X 2= 1 0.0000 a-4=1

(0.6875)10 = (0.1011)2

decimal to octal
Decimal to Octal

Similar to decimal  binary.

  • Find largest power-of-8 smaller than decimal number
  • Divide by power-of-8. The integer result is Octal digit.
  • The remainder is new decimal number.
  • Do the same thing again
decimal octal
Decimal  Octal
  • Convert decimal 153 to Octal

512 is too large, so use 64

Octal  200

Decimal  153 – 64X2 = 25

Next is 8

Decimal  25 – 8X3= 1

Octal  230

Decimal  1 – 1X1 = 0

Next is 1

Octal  231

decimal octal fraction
Decimal  Octal (Fraction)
  • Convert decimal 0.513 to Octal

Integer Fraction Coefficient

0.513 X 8 = 4 + 0.104 a-1=4

0.104 X 8 = 0 + 0.832 a-2=0

0.832 X 8 = 6 + 0.656 a-3=6

0.656 X 8 = 5 + 0.248 a-4=5

0.248 X 8 = 1 + 0.984 a-5=1

0.984 X 8 = 7 + 0.872 a-5=7

(0.513)10= (0.406517)8

binary to octal
Binary to Octal
  • Partition Binary number into group of three digits each
  • The corresponding octal digit is then assigned to each group
  • (10 110 001 101 011 . 111 100 000 100)2
  • (10 110 001 101 011 . 111 100 000 100)2 = (26153.7460)8
octal to binary
Octal to Binary
  • Each Octal digit is converted to its three digit binary equivalent
  • (26153.7460)8 = (010 110 001 101 011 . 111 100 000 100)2
hex to binary

0010

1010

1100

Hex to Binary
  • Convention – write 0x before number
  • Hex to Binary – just convert digits

0x2ac

0x2ac = 001010101100

No magic – remember hex digit = 4 bits

binary to hex

5

3

7

b

Binary to Hex
  • Just convert groups of 4 bits

101001101111011

1011

0101 

0011

0111 

101001101111011 = 0x537b

hex to decimal
Hex to Decimal
  • Just multiply each hex digit by decimal value, and add the results.

0x2ac

2 • 256

+ 10 • 16

+ 12 • 1

= 684

decimal to hex
Decimal to Hex

Similar to decimal  binary.

  • Find largest power-of-16 smaller than decimal number
  • Divide by power-of-16. The integer result is hex digit.
  • The remainder is new decimal number.
  • Do the same thing again
decimal to hex1
Decimal to Hex

684

0x2__

684/256 = 2

684%256 = 172

0x2a_

172/16 = 10 = a

0x2ac

172%16 = 12 = c

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