Chapter 2 continued

• Combinational Circuits Continued
  • Transistors
    • All of our logical circuits are built from transistors
    • TRANsfer reSISTOR
    • 
    • When a positive charge is applied to the base, electrons flow from the emitter to the collector
    • When zero voltage is applied to the base, electrons can not flow.
    • Electrons flow from ground to a voltage source.
    • 
    • The above diagram represents a not gate.

      Vi	Vo
      0 V	+5 V
      +5 V	0 V

    • In some way, we are looking for a potential flow from the output line.
    • 
    • This is a nor circuit
    • 
    • This is a nand circuit
  • Universal Gates
    • As we saw above, we can construct simple gates from transistors.
    • These can construct simple nand, nor, and not gates.
    • nand
      • Not And
      • 

      • x	y	x nand y
        0	0	1
        0	1	1
        1	0	1
        1	1	0

    • nor
      • Not Or
      • 

      • x	y	x nor y
        0	0	1
        0	1	0
        1	0	0
        1	1	0

    • equiv
    • Not xor
    • 

    • x	y	x equiv y
      0	0	1
      0	1	0
      1	0	0
      1	1	1

    • These gates are called universal because all other gates can be constructed using only nand or only nor gates.
  • Generalized and and or Gates
    • We can extend our basic gates to allow more inputs.
    • These are called generalized gates.
    • They Have the same propagation delay.
    • They take up more space.
    • 
    • Why do we want this?
      • We can express the output of the full adder in Boolean algebra
      • 
      • We can solve these equations algebraically.
      • Look for a complete list of rules on page 45.
      • 
      • Notice, the final expression (although more complex) is a sum of products.
      • This represents a two level circuit
      • 
      • And this has a propagation delay of one gate less than our outer circuit.
      • Here we are trading space for speed.
      • The sum of products form is known as disjunctive normal form
      • Every boolean expression can be written in this form.
      • Unfortunately, there is only a limited number of gates we can send a signal to before we need to boost the signal.
      • This is called the fan out problem

  • Integrated Circuits
    • IC for short
    • An IC is a collection of gates on one chip
    • DIP - dual in-line package
    • 
    • SIP - single in-line package
    • Signal leads are not shielded, and cannot cross.
    • This limits the ability to get signals in-to/out-of the chip
    • This is called the Pin Limitation Problem
    • Levels of chip design
      • SSI - small scale integration
        • 1-10 gates
        • Example to pass around.
        • Four gates on the same chip
      • MSI - medium scale integration
        • 10-100 gates
        • Multiplexer
          • Example:
          • Four inputs for data
          • Two inputs for control
          • One output
          • Based on the values of the control line, one of the data lines is selected for output.
          • 
          • 

          • c1	c0	o
            0	0	i0
            0	1	i1
            1	0	i2
            1	1	i3

          • This is a 4-1 multiplexer
          • A demultiplexer takes 1 input and n signals and supplies a value to one of 2ⁿ output lines
      • LSI - large scale integration
        • 100 - 10,000 gates
        • Programmable Logic Arrays
      • VLSI - very large scale integration
        • 10,000 +, keeps going
        • Microprocessors.
        • Current processors have up to 250 million transistors