SI232 Slide Set #6: Digital Logic (Appendix B) 1 2 Appendix - - PowerPoint PPT Presentation

si232 slide set 6 digital logic appendix b
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SI232 Slide Set #6: Digital Logic (Appendix B) 1 2 Appendix - - PowerPoint PPT Presentation

ADMIN Very different material! Reading Appendix: Read B.1, B.2, B.3. Skim B.5. SI232 Slide Set #6: Digital Logic (Appendix B) 1 2 Appendix Goals Logic Design Digital Signals Establish an understanding of the basics of


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SLIDE 1

1

SI232 Slide Set #6: Digital Logic (Appendix B)

2

ADMIN

  • Very different material!
  • Reading

– Appendix: Read B.1, B.2, B.3. Skim B.5.

3

Appendix Goals Establish an understanding of the basics of logic design for future material

  • Gates

– Basic building blocks of logic

  • Combinational Logic

– Decoders, Multiplexors, PLAs

  • Clocks
  • Memory Elements
  • Finite State Machines

4

Logic Design – Digital Signals

  • Only two valid, stable values

– False = – True =

  • Vs. voltage levels

– Low voltage “usually” – High voltage “usually” – But for some technologies may be the reverse

  • How can we make a function with these signals?
  • 1. Specify equations:
  • 2. Implement with
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SLIDE 2

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Boolean Algebra

  • One approach to expressing the logic function
  • Operators:

– NOT

Output true if

– AND: ‘A logical product’

Output true if

– OR : ‘A logical sum’

Output true if

– XOR

Output true if

– NAND

Output true if

– NOR

Output true if

A x = AB B A x =

  • =

B A x + = B A x ⊕ =

B A x

  • =

B A x + =

6

Gates

7

Example

A(1) C(0) D(1) B(1) G

Equation: 8

Truth Tables Part 1

  • Alternative way to specify logical functions
  • List all outputs for all possible inputs

– n inputs, how many entries? – Inputs usually listed in numerical order

A x = B A x + =

A x 1 1 A B x 1 1 1 1 1 1 1

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SLIDE 3

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Truth Tables Part 2

  • Not just for individual gates
  • Not just for one output

F 1 1 1 1 1 1 1 1 1 1 1 1 G C B A

A C B G F

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Exercise #1

  • Show the truth table for NAND and NOR gates

A B x 1 1 1 1 A B x 1 1 1 1

NOR NAND

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Exercise #2

  • A.) Show the truth table for the following logic circuit

A B C y

y C B A

  • B.) Write the Boolean equation for this circuit.

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Exercise #3

  • Draw a circuit for the following formula:

F = ( (A + B) C ) + D

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SLIDE 4

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Exercise #4 – For more thought

  • Recall – how many entries are in a truth table for a function with n

inputs?

  • Consider – how many different truth tables are possible for a function

with n inputs?

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Laws of Boolean Algebra

  • Identity Law
  • Zero and One Law
  • Inverse Law
  • Commutative Law

A A = + 0

1 1 = + A

0 =

  • A

1 = + A A =

  • A

A A B B A + = +

A B B A

  • =
  • A

A =

  • 1

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Laws of Boolean Algebra

  • Associative Law
  • Distributive Law
  • DeMorgan’s Law

C B A C B A + + = + + ) ( ) ( C B A C B A

  • =
  • )

( ) ( ) ( ) ( ) ( C A B A C B A +

  • +

=

  • +

) ( ) ( ) ( C A B A C B A

  • +
  • =

+

  • B

A B A

  • =

+ B A B A + =