Basic Gates

• This is partially from appendix B.
• We are beginning combinational logic or logic which does not contain memory.
• Sequential logic is the opposite, logic that contains a memory.
• I will demo with tkgate because I like it.
  • tkgate on sourceforge
  • I don't think there is a windows version.
  • You might try Digital
• For us, the basic components of logic are
  • not
  • and
  • or
• We will also be using these support devices
  • Switches
  • LEDs
  • tri-state devices
  • This appears to be called a driver in Digital.
• Logic is not electronics.
  • We are at a weird mixture between the two, but
  • Think about vdd as a source of true
  • Think about ground as a source of false.
  • This is wrong, but it will work.
• Each of the logic component can be expressed three ways
  • Boolean Expression
  • Truth Table
  • Symbol
• You should be able to switch between the three.
• Not
  • $f(x) = \overline{x}$
  • In logic it might be $f(x) = \neg x$

  • $x$	$\overline{x}$
    0	1
    1	0

  • 
  • The datasheet for a not chip.
  • Generally we think of not as having less than a unit cost.
• and
  • $f(a,b) = a \cdot b = ab$
  • In logic $f(a,b) = a \land b$

  • a	b	ab
    0	0	0
    0	1	0
    1	0	0
    1	1	1

  • 
  • The datasheet for similar chips.
• or
  • $f(a,b) = a + b = ab$
  • In logic $f(a,b) = a \lor b$

  • a	b	ab
    0	0	0
    0	1	1
    1	0	1
    1	1	1

  • 
• And and or are counted as single units in delay terms.
• There is an exclusive or. (xor)
• nand and nor are inverted versions of and and or.
  • 
  • These are just an and or or gate negated.
  • It is common to put a dot in place of a inverter or not gate.
• Crossing the wires
  • If wires just cross, they do not make a connection.
  • If wires have a dot at the intersection, they make a connection.
  • 
• Tristate
  • This allows us to control what comes out of a circuit.
  • Think putting something on the buss.
  • This can be built out of transistors.
  • 
  • It has
    • A data input wire
    • A data output wire
    • A control line
    • If the control line is high, the data from the input is passed to the output.
    • If the control line is low, nothing is passed to the output.
• More than two input and/or gates
  • For or, if any one is true, the entire thing is true.
  • For and, if any one is false, the entire thing is false.
  • 
• Bundled wires
  • Sometimes we wish to run multiple bits through a device.
  • We do this with bundled wires.
  • 
  • We indicate the number of wires with a slash and a number
• I am sure that I have forgotten something, but we will deal with it as it arises.