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5.5 Logic circuits

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5.5 Logic circuits

  1. 1. Module 5: Digital Techniques and Electronic Instrument Systems 5.5 Logic Circuits
  2. 2. Digital Systems Hardware Design Flow  1. System Level Design  2. RTL Design  3. Physical Design  4. Layout synthesis  5. The final circuit
  3. 3. Gates AND - OR - NOT x y f 0 0 0 0 1 0 1 0 0 1 1 1 x f 0 1 1 0 AND NOT (Inverter) x y f 0 0 0 0 1 1 1 0 1 1 1 1 OR f = x + yf = xy
  4. 4. Gate NAND x y f = xy 0 0 0 0 1 0 1 0 0 1 1 1 AND x y f = xy 0 0 1 0 1 1 1 0 1 1 1 0 NAND
  5. 5. Gate NOR x y f = x+y 0 0 1 0 1 0 1 0 0 1 1 0 NOR x y f = x+y 0 0 0 0 1 1 1 0 1 1 1 1 OR
  6. 6. Analyzing a digital circuit (1/2) x y f = xy + xy 0 0 0 0 1 1 1 0 1 1 1 0
  7. 7. Gate EXOR x y f = xy + xy 0 0 0 0 1 1 1 0 1 1 1 0
  8. 8. Analyzing a digital circuit (2/2) x y S C 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1  Half-adder: Adds two bits.
  9. 9. Full Adder x y Cn-1 S C 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1
  10. 10. Fan-In and Fan-out  Fan-In: the number of digital inputs of a digital circuit.  Fan-Out: the number of digital outputs of a digital circuit.
  11. 11. From a Digital Circuit to the Truth Table  1st way:  Apply all possible inputs to the circuit and fill the Truth Table.  2nd way:  Find the Boolean expression and determine the output for each Truth Table record.
  12. 12. From the Truth Table to the Digital Circuit x y z f 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 x/ yz 00 01 11 10 0 1 1 0 0 1 1 1 0 1 Which variables do not vary in this team? y, which is “0”. Which variables do not vary in this team? All y΄ So: f = xyz΄ + y΄ xyz΄

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