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Today’s Agenda

Today’s Agenda. Introduction to Digital Electronics. Analogue Systems Use analogue signals (or Continuous Signals) Analogue signals can take any value within a range E.gs Mechanically designed clock Analogue meter display Digital Systems Use digital signals (or Discrete Signals)

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Today’s Agenda

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  1. Today’s Agenda Introduction to Digital Electronics

  2. Analogue Systems • Use analogue signals (or Continuous Signals) • Analogue signals can take any value within a range • E.gs • Mechanically designed clock • Analogue meter display • Digital Systems • Use digital signals (or Discrete Signals) • Digital signals can take only a limited number of values (discrete values), usually just two values are used: the positive supply voltage (+Vs) and zero volts (0V). • E.gs • Digital Clock • Digital meter display

  3. Analogue Systems • Analogue Meter Display

  4. Digital Systems • Digital Meter Display

  5. Noise in Analogue or Digital Systems • 'noise' is unwanted signal mixed in with the desired signal • for example an audio amplifier may pick up some unwanted signal 'hum' • Noise is difficult to eliminate from analogue signals because it may be hard to distinguish from the desired signal.

  6. Noise in Digital Systems • Noise is relatively easy to eliminate from digital signals because it is easy to distinguish from the desired signal which can only have particular values. • For example: if the signal is meant to be +5V (true) or 0V (false), noise with voltage between 0 to 5V can be easily identified.

  7. Digital Systems • Use discrete signals which can have only two values. • Such signals are also called as logic signals. • These two values are +V voltage or 0V voltage.

  8. Logic Gates • Logic gates process logic signals which represent true or false signals. • Gates are identified by their logical function. • Different logical functions are • NOT, AND, OR, XOR, NAND, NOR

  9. Truth Table • A truth table is a good way to show the function of a logic gate. • It shows the output states for every possible combination of input states. • The symbols 0 (false) and 1 (true) are usually used in truth tables.

  10. NOT Gate (Inverter) • The output Q is true when the input A is NOT true • the output is the inverse of the input: Q = NOT A Truth Table

  11. AND Gate • The output Q is true if input A AND input B are both true: Q = A AND B • An AND gate can have two or more inputs and its output is true if all inputs are true.

  12. OR Gate • The output Q is true if input A OR input B is true (or both of them are true): Q = A OR B • An OR gate can have two or more inputs and its output is true if at least one input is true.

  13. NAND gate (NAND = Not AND) • Q = NOT (A AND B)

  14. NOR gate (NOR = Not OR) • Q = NOT (A OR B)

  15. EX-OR (EXclusive-OR) gate • Q = (A AND NOT B) OR (B AND NOT A) • Q = AB’ + A’B

  16. EX-NOR (EXclusive-NOR) gate • Q = (A AND B) OR (NOT A AND NOT B) • Q = AB + A’B’

  17. Boolean Algebra • It is a deductive mathematical system that deals with binary variables and logical functions. • Boolean Expressions can be made from binary variables and logical operations. • These boolean expressions are then converted to digital circuit. • Boolean expression can also be represented in the form a truth table.

  18. Given a truth table write the boolean expression and draw the circuit

  19. f0 = x’y’z + xy’z’ + xyz • To get f0’ (complement of f0) apply DeMorgan’s law • DeMorgan’s law (x+y)’ = x’.y’ (xy)’ = x’ + y’ • f0’ = (x’y’z + xy’z’ + xyz)’ • f0’ = (x+y+z’)(x’+y+z)(x’+y’+z’)

  20. Example digital circuits • Design digital circuit for 1-bit Comparator. • Given 3-bit number. Design a digital circuit that tells whether the number is even or odd. Output should be 1 if the number is even and 0 if number is odd. • Design digital circuit for 2-bit Comparator.

  21. Postulates and Theorems of Boolean Algebra • x + 0 = x • x + x’ = 1 • x + x = x • x + 1 = 1 • (x’)’ = x • x+y = y+x • x+(y+z) = (x+y)+z • x(y+z) = xy + xz • x+xy = x • x . 1 = x • x . x’ = 0 • x . x = x • x . 0 = 0 • xy = yx • (xy)z = x(yz) • x + (yz) = (x+y)(x+z) • x(x+y) = x

  22. Digital Circuits • Combination Circuits • These are the digital circuits which takes external input, process the input in the circuit and produce the output based on the present input provided to it. • Sequential Circuits • These circuits takes external input and present state of storage elements, processes the entire input and produces the output. • Here the output depends on both the input and the storage element.

  23. Digital systems are made using both combinational as well as sequential circuits. • Example: Central Processing Unit • Consist of ALU, Register File, Memory, decoders, multiplexers etc.

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