Engineering Lecture 3 Digital Electronics

1
Engineering Lecture 3 Digital Electronics
by Jaroslaw Karcz
2
Overview

• BASIC LOGIC CONCEPTS
• COMBINATIONAL LOGIC
• SEQUENTIAL LOGIC

3
1. BASIC LOGIC CONCEPTS
Analogue Signals

• Representation of a quantity that varies over a
  continuous range of
• values
• e.g. sound, light, temperature, and pressure

• These may be represented electrically by an
  analogue voltage/current
• A device that is used to convert an analogue
  signal into an analogue
• voltage or current is known as a transducer  
    

4
Digital Signals

• Representation of a quantity that varies in
  discrete steps over a range of values

5
Logic States

• Digital Electronics circuits in which only 2
  states possible at any point
• e.g. transistor can either be in saturation
  or be non-conducting
• Choose to talk about voltages, calling a level
  HIGH or LOW
• Depending on context, can be represented as
  following for example

• Digital Electronics circuits in which only 2
  states possible at any point
• e.g. transistor can either be in saturation
  or be non-conducting
• Choose to talk about voltages, calling a level
  HIGH or LOW
• Depending on context, can be represented as
  following for example

• one bit (binary digit) of a number (0 or 1)
• whether switch is opened or closed
• whether signal is present or absent
• some analogue level is above/below some preset
  limit (threshold)
• whether some event has occurred yet
• whether some action should be performed
• etcetera.

• one bit (binary digit) of a number (0 or 1)
• whether switch is opened or closed
• whether signal is present or absent
• some analogue level is above/below some preset
  limit (threshold)
• whether some event has occurred yet
• whether some action should be performed
• etcetera.

• HIGH and LOW states represent the TRUE and
  FALSE states of
• Boolean logic, in some predefined way

6
Analogue to Digital Conversion

• In real world, signals appear in analogue form.
• It is often desirable to convert continuous
  (analogue) data to digital (discrete) form
• Conversion to digital format requires definition
  of threshold values
• e.g.
• in electronics, the voltage levels corresponding
  to HIGH or LOW are allowed to fall in some range
  
• Typical LOW- and HIGH-state output voltages are
  usually within
• a tenth of a volt of 0 and 5 volts,
  respectively

7
2. COMBINATORIAL LOGIC

• Circuits composed of combinations of logic gates,
  
• with NO FEEDBACK from outputs to inputs

8
Gates and Truth Tables - BASIC
The AND gate
IEEE /ANSI Symbol
Older (Mil-Spec) Symbol

• Output is HIGH (1) if and only if all inputs
  are HIGH (1).
• If any input(s) are LOW (0), the output is
  guaranteed to be in a LOW state

9
Gates and Truth Tables
Gates and Truth Tables
Gates and Truth Tables
Gates and Truth Tables - BASIC
The OR gate
The OR gate
The OR gate
The OR gate

• ..\Pictures\Digital Gates\or.gif

• Output will be HIGH (1) if any of the inputs
  are HIGH (1)
• Output goes LOW (0) if and only if all inputs
  are LOW (0).

• Output will be HIGH (1) if any of the inputs
  are HIGH (1)
• Output goes LOW (0) if and only if all inputs
  are LOW (0).

10
Gates and Truth Tables - BASIC
The NOT gate (inversion)
Also denoted as X inverse of X

• Whatever logical state is applied to the input,
  the opposite state will
• appear at the output

11
Gates and Truth Tables - DERIVED
The NAND gate
(derived from AND NOT gates)

• With the gate shown above, both inputs must have
  logic 1 signals applied to them in order for the
  output to be a logic 0.
• With either input at logic 0, the output will be
  held to logic 1.

12
Gates and Truth Tables - DERIVED
The NOR gate (same principle applies)

• NOR gate is an OR gate with the output inverted
• Where OR gate allows the output to be HIGH (1),
  if any input is true, the NOR gate inverts this
  and forces the output to logic 0 (LOW).

13
Gates and Truth Tables still more??
The XOR gate

• Output HIGH when inputs are inverses of each
  other

The XNOR gate

• Output HIGH when inputs are exactly the same

14
3. SEQUENTIAL LOGIC

• Use of devices in such a manner that the new
  state of an output may depend not only on the
  existing state of its inputs, but also on
  previous conditions imposed upon the inputs. In
  other words, capacity for MEMORY
• This allows for construction of devices such
  as
• Counters
• Arithmetic Accumulators
• Frequency Dividers, etc.
• The most fundamental unit of sequential logic
  is the FLIP-FLOP

15
Operation of NAND Gate Flip-Flop
Setting the latch
The time sequence displays the conditions under
which the set (S) and reset (R) inputs cause a
state change, and those for which they remain
unaltered.
16
Flip-flops

• D Flip-flop

Divide-by-2-Circuit
Ripple-Down Counter
17
Flip-flops

• J-K Flip-flop

Truth Table

• Q indicates the value of Q after the next clock
  pulse (output only changes upon
• a particular state of the clock pulse) here
  PGT
• If J and K are different, Q takes on the value
  of J
• If J and K are both 0, Q remains unchanged
• If J and K are both 1, Q changes to its inverse
  (it "toggles")
• Information from J and K is read in on the
  rising edge of the clock, and is
• translated into action at the Q outputs on the
  FALLING edge of the clock

18
Applications of Flip-flops
Synchronous Counter (created through use of
T-flip flop slightly modified J-K Flip-Flop)
T-Flip Flop
19
Applications of Flip-flops

• Data Register

• A circuit which can store temporarily all bits of
  a binary number

Anatomy of Data Register composed of D
Flip-flops
Symbol
3-bit register
(a typical personal computer will have
several 16-bit and 32-bit data registers in its
arithmetic unit)