ELEC1303 - Lecture 1

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Introductory Concepts - Slides

Digital vs Analog

• Digital $-$ information is represented by signals which take on values that correspond to a finite number of discrete information values
• Analogue $-$ a continuous range of signal values correspond to a continuous range of information values

What is a Digital System?

• A digital system takes in digital values and then outputs digital values

Digital Systems use Binary Values

• Each binary digit (called a bit) is either 1 or 0
• Bits have no inherent meaning
• Binary is popular because:
  • Transistors, the basic digital electric components, operate as switches (on/off) using only two voltages (high/low)
  • Storing/transmitting one of two values is easier than three or more (e.g., loud beep or quiet beep)

Better Noise Immunity

Analog to Digital Conversion

• Real world is analog but analog signals can be converted to digital
  • e.g. a microphone taking your voice as input
• This is done by taking measurements or “samples” of the continuously varying signal at regular intervals
  
• Amplitude Quantization
  • Quantization noise leads to an irreversible corruption of the signal
  • More quantization levels → more closely original signal is reproduced
• Encoding
  • Assign a unique binary code to each quantization level
    • 2 bits required for $4=2^2$ quantization levels
      e.g. 00, 01, 10, 11, etc.
    • N-bit code can represent $2^N$ quantisation levels

Really easy trick for binary pattern in lecture recording

Brief recap:

• Each column follows a pattern with $x$ 0’s followed by $x$ 1’s that repeat
• $x=2^{n-1}$ for the column with the $n$th position
• e.g. the first column of binary has $x=2^0=1$
  i.e. the pattern is one 0, then one 1, before repeating

Digital Number Systems

• Radix is another word for base
• Hexadecimal (base 16) is used to represent large binary numbers
  • Goes from 1-9 and then followed by A-F
  • Group bits 4 at a time starting from the right
    

Express ${\text{1A2F}}_{16}$ in decimal:
Start by writing the column weights:
$16^3,16^2,16^1,16^0$
$4096,256,16,1$
Multiply by digit:
$1(4096)+10(256)+2(16)+15(1)=6703_{10}$

Two Types of Digital Systems

• Combinational systems are memoryless
  • Output depends only on present inputs
• Sequential systems have memory
  • Outputs depend on the present inputs and on the previous inputs
  • Memory content can also change as the circuit runs
  • e.g. combination locks, elevators, traffic lights and computers!

Microprocessor

• Most sophisticated digital system available
• Found in a wide range of products

Transistor as Switches

• Modern digital systems are designed in CMOS technology
  • MOS stands for Metal-Oxide on Semiconductor
  • C stands for complementary because there are both normally-open and normally closed systems
• MOS transistors act as voltage controlled switches:
  • NMOS
    • If voltage is “1” (sufficiently high) then conducting path established
  • PMOS
    • If voltage is “0” (sufficiently low) then conducting path established
  • NMOS/PMOS transistors act as complimentary switches

Benefits of Digital Circuits

• Tolerance to noise
• Reproducibility of information
• Flexibility and functionality
  • Easier to store, transmit and manipulate information
• Shorter time to market
  • Easier to design
• Digitisation results in smaller, faster and cheaper circuits

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ELEC1303 - Lecture 2