CHAP 3

• Boolean logic


  Logic gates made of transistors
• Logic gates


  • They are the basic components of integrated circuits (IC)
  • Small-Scale Integration (SSI): an IC that has less than 10 gates
  • Medium-Scale Integration (MSI): between 10 and 100 gates such as decoders and multiplexers
  • Large-Scale Integration (LSI): contains between 100 and 1000 gates
  • Very-Large-Scale Integration (VLSI): more than 1000 gates
• A microprocessor is primarily a complex digital logic circuit
• How logic gates are made

  1. Computers use Complementary MOS (CMOS) technology (made of both n-type and p-type transistors)

  2. Design of NOT gate

  
• AND logic


  Z=XY
• OR logic


  Z=X+Y
• NOT logic


  Z=X
• XOR logic


  Z=X⊕Y
• Three state device


  Has an open circuit output state in addition to 0 and 1
• Boolean theorems


  • X+X=X
  • X+1=1
  • X+0=X
  • X+X'=1
  • XX=X
  • X.1=X
  • XX'=0
  • (X')'=X
• Distributive Theorem


  X(Y+Z)=XY+XZ
• De Morgan's Theorem I


  (X+Y)'=X'Y'
• De Morgan's Theorem II


  (XY)'=X'+Y'
• Commutative Law


  X+Y=Y+X
• Associative Law


  X(YZ)=(XY)Z

  X+(Y+Z)=(X+Y)+Z
• Karnaugh Maps


  1. Used to simplify Boolean functions without using Boolean theorems

  2. Transfer function to K-map and read simplified function from K-map