Computer Digital Electronic

1.1 Introduction to digital 1s and 0s

• A large part of the worldwide telecommunications system falls in the category of digital systems — used two states to represent information:
  • Telegraph system
    • short & long electric pulses
  • Morse code
    • dots & dashes
• Timing diagram is used to represent the state at a given time timing diagram
  • Voltage vs time
  • Can be produced by oscilloscope and logic analyzer

1.2 Digital signals

• Transition between two states (1 → 0 or 0→1) is called edge
• Digital circuits have input and output of 0 and 1
• If a system operates such that the time for a complete cycle is constant, it’s called a periodic system.

1.3 Logic circuits and evolving technology

• The manner which a digital circuit responds to an input is called the circuit’s logic
• Digital circuits of today’s technology are implemented using integrated circuits (ICs) that are tailor-made for their specific function.

1.4 Numerical representations

• Physical systems use quantities which must be manipulated arithmetically
• Quantities can be represented numerically in:
  • Analog form - continuous variable
    • Sound through microphone causes voltage changes
    • speedometer changes with speed
    • mercury thermometer changes value with temperature
  • Digital form - varies in discrete steps
    • digital clock changes number for each time
    • digital thermometers show changes at least for one degree

1.5 Digital and analog systems

• What is digital systems?
  • A combination of devices that manipulate logical information or physical quantities represented in digital form
  • quantities can take only discrete values
  • What are the benefits of digital systems?
    • Ease of design
    • Well suited for storing information
    • Accuracy, precision are easy to maintain
    • Programmable operation
    • Less affected by noise
    • Ease of fabrication(manufacturing) on IC chips
  • What are the limits of a digital techniques?
    • The analog nature of the world requires time-consuming conversion process
      • Convert the physical variable to an electrical signal (analog)
      • Convert the analog signal to digital form
      • Process the digital information
      • Convert the digital output back to real-world analog form
• What is analog system?
  • A combination of devices that manipulates physical quantities represented in analog form.
  • Quantities can vary over a continuous range of values
• Why shift to digital system?
  • Digital systems are easier to design
  • Information storage is easy
  • Accuracy, precision are easier to maintain
  • Operations can be programmed
  • Digital circuits are less affected by noise
  • More digital circuitry can be fabricated on IC chips

1.6 Digital number systems

• Numbering systems:
  • Decimal - 10 symbols
  • Hexadecimal - 16 symbols
  • Octal - 8 symbols
  • Binary - 2 symbols

1.7 Representing binary quantities

• How does analog signal converted into digital?
  • Taking measurements of the continuously varying signal at regular intervals
• Examples of two state devices:
  • light bulb (off or on)
  • diode (conducting or not conducting)

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  • relay (energized or not energized)
  • transistor (cutoff or saturation)
  • photocell (illuminated or dark)

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1.8 Parallel and serial transmission

• What is parallel transmission?
  • All bits are transmitted simultaneously
• What is serial transmission?
  • Each bit is transmitted per some time interval

1.9 Memory

• What is memory
  • A circuit that retains a response to a momentary input (if it’s 1, it’ll keep it that way until it is changed)
• What are memory elements?
  • magnetic, optical, electronic latching circuits

1.10 Digital computers - What is a computer? - a system of hardware that performs arithmetic operations, manipulates data, makes decisions - it performs operations based on the instructions in teh form of a program at high speed, and a high degree of accuracy - What are the major parts in a computer?

    ![Screenshot 2023-06-21 at 11.25.36 AM.png](images/university-notes/CDE/Screenshot_2023-06-21_at_11.25.36_AM.png)

    - Input unit - process interactions and data
    - Memory unit - stores data and instructions
    - Control unit - interprets instructions and send appropriate signals to other units as instructed
    - Arithmetic/ logic unit -  performs arithmetic calculation and logical decisions
    - Output unit - presents information form the memory to the operator or process
- What are the types of computers?
    - Microcomputer - desktop PCs
    - Minicomputer
    - Mainframe
    - Microcontroller

• summing
• Double-dabble method

• 1st method
• 2nd method

• Hex to decimal
• Decimal → hex
• Hex → binary
• Binary → hex
  • Binary is grouped to a group of 4, start converting from the LSB (most right-side)
  • Add zeros to LSB to make it 4 bits

• A way to present decimal numbers in binary form

• Used in app where numbers change rapidly

• 8 bits = 1 byte
• 4 bits = 1/2 byte = nibble
• word - a group if bits that represents a certain unit of information
  • word size - number of bits in the binary word a digital system operates on — PC = 64bits

• represents characters and functions found on a computer keyboard:
  • 26 lowercase
  • 26 uppercase
  • 10 digits
  • 7 punctuation marks
  • others
• consist of 7 bit, 2^7 = 128 possible codes.

• Binary codes are frequently moved between locations, electrical noise can cause errors during transmission
• How to detect the error?
  • using the parity method
  • add an extra bit to a code group, called the parity bit, can be 0 or one depending on the number of 1s in the code group
  • The receiver then’ll calculate, if even/ odd, that means the code is not corrupted
  • weakness:
    • If the parity method is even (1011101), and there’s error that turns the code into even (11111111), the receiver’ll interpret it as no error, since it’s even.
  • Parity methods:
    • Even
      • The total number of bits including the parity bit must be even number
      • eg: binary group 1011 → 11011 — parity bit added to the beginning(can also be at the end) to make number of 1s even
    • Odd
      • The total number of bits including the parity bit must be odd number
      • eg: binary group 1111 → 11111 — parity bit added to the beginning(can also be at the end) to make number of 1s even

• A device that acts as a building block for digital circuits (the green boards)

• AND
  • Only if both is true, the output is true
• OR
  • One input is true, output is true
  • may be asked on exam, label the component
• NOT
  • Also called as logical inverter (Invert the value)
• XOR (exclusie-OR)
  • Only true if one is true, (True if input 1 and 2 is different)
• NAND (NOT AND)
  • Invert the and logic
• NOR (NOT OR)
• XNOR (NOT XOR)
  • True if the input is same, false if the inputs are different
  • The most popular logic gate

• How to represents a negative value?
  • +12 is 01100
  • do 1’s complement (change 1→0 and vice-versa): 10011
  • add 1 = 10100
  • hence -12 = 10100 (since the leftmost bit is 1, means its is -16+4 =-12)
  • Why use these?
    • If there is a substraction operation, it can be represented by plus a negative number
    • eg; 12-3 = 12+(-3)
    • Hence, the complexity can be reduced
• Slide
  • To show +ve sign, 0 is added
  • To show -ve sign, 1 is added
  • What is 2’s complement system?
    • to represent signed number
    • f number is +ve (leading 0), the 2’s complement is the same as the original number
    • steps:
      • Perform bit inversion, eg; 1101 → 0010
      • Add 1 to result, eg: 0010 + 1→ 0011
    • Why use 2’s complement?
      • (+ve bit) - (-ve bit) = (+ve )+ (negate -ve bit) — no need for a separate operation for a substraction (unified approach)

• when start to the next number of multiplication, move left by on(add zero to the right side)