Circuits

• Circuits are constructed from gates
• Circuits who's input completely determines their output are known as Combinational Circuits
• Circuits with a feedback loop, or who's input does not completely determine their output are Sequential Circuits
• Combinational circuits are what we will look at the most in this class.
• When drawing a circuit, if two wires are connected, we put a dot.
• IF there is no dot, we assume they cross, but are not connected.
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• What does this circuit do?
  • We could run it and see
  • We could construct a truth table
  • We could try to do some algebra
• Boolean Algebra
  • Invented by George Bool (see box p 89)
  • Two values for each variable

  • Property	AND	Or
    Commutative	AB = BA	A+B = B+A
    Associative	(AB)C = A(BC)	(A+B)+C = A+(B+C)
    Distributive	A(B+C)= AB+AC	A+BC = (A+B)(A+C)
    Identity	A1 = A	A+0 = A
    Complement	AA' = 0	A+A' = 1
    DeMorgan's Law	(AB)' = A'+B'	(A+B)' = A'B'

  • So our circuit becomes
    • X = AB + AC
    • X = A(B+C) (Associative law)
    • We could prove this with a truth table
    • 
    • This circuit uses three fewer transistors.
• Design a circuit for a n bit adder
  • Discuss Algorithm for adding 2 bits
  • Truth table for a half adder
  • Draw half adder
  • Discuss algorithm for adding three bits
  • Truth table for an adder
  • Draw Circuit full adder
  • 
  • Discuss algorithm for adding 2 n bit numbers
  • Circuit for ripple carry adder
• Ondjre's Adder
  • Built from ssi chips (Small Scale Integration)
  • 4 and gates on a chip (74als08n)
  • 1Y = 1A and 1B
  • GND is a ground pin
  • Vcc is a +5v power source
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• Integrated Circuits
  • SSI - 1 to 10 Gates on a chip
  • MSI - 10 to 100 gates on a chip
  • LSI - up to 100,000 gates on a chip
  • VLSI - More than 100,000 gates on a chip
• Sequential Circuits
  • Memory, clock, others
  • Have a feedback loop.
  • RS Flipflop
    • 
    • S - sets - output of Q is 1
    • R - reset - output of Q' is 1
  • This is just one of many different types of flip-flops
  • From these, we build memory and registers
• Pentium 4 information
  • 125 million transistors