1 / 10

ICS 241

ICS 241. Discrete Mathematics II William Albritton, Information and Computer Sciences Department at University of Hawai’i at Manoa For use with Kenneth H. Rosen’s Discrete Mathematics & Its Applications (5 th Edition) Based on slides originally created by

carla-bradley
Download Presentation

ICS 241

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ICS 241 • Discrete Mathematics II • William Albritton, Information and Computer Sciences Department at University of Hawai’i at Manoa • For use with Kenneth H. Rosen’s Discrete Mathematics & Its Applications (5th Edition) • Based on slides originally created by • Dr. Michael P. Frank, Department of Computer & Information Science & Engineering at University of Florida

  2. Section 10.3 – Logic Gates • Inverter, Or, And gate symbols. • Multi-input gates. • Logic circuits and examples.

  3. Logic Gate Symbols x • Inverter (logical NOT,Boolean complement). • AND gate (Booleanproduct). • OR gate (Boolean sum). • XOR gate (exclusive-OR,sum mod 2). x x·y y x x+y y x x⊕y y

  4. Multi-input AND, OR, XOR • Can extend these gates to arbitrarilymany inputs. • Two commonlyseen drawing styles: • Note that the second style keeps the gate icon relatively small. x1 x1x2x3 x2 x3 x1⋮ x5 x1…x5

  5. Class Exercise • Exercise 3. (p. 718) • Each pair of students should use only one sheet of paper while solving the class exercises

  6. NAND, NOR, XNOR • Just like the earlier icons,but with a small circle onthe gate’s output. • Denotes that output is complemented. • The circles can also be placed on inputs. • Means, input is complementedbefore being used. x y x y x y

  7. Buffer x x • What about an invertersymbol without a circle? • This is called a buffer. It is the identity function. • It serves no logical purpose, but it represents an explicit delay in the circuit. • This is sometimes useful for timing purposes. • All gates, when physically implemented, incur a non-zero delay between when their inputs are seen and when their outputs are ready.

  8. Combinational Logic Circuits • Note: The correct word to use here is“combinational,” NOT “combinatorial!” • Many sloppy authors get this wrong. • These are circuits composed of Boolean gates whose outputs depend only on their most recent inputs, not on earlier inputs. • Thus these circuits have no useful memory. • Their state persists while the inputs are constant, but is irreversibly lost when the input signals change.

  9. Combinational Circuit Examples • Examples • Light controlled by two switches • Half adder using OR/AND/NOT • Full adder from half-adders

  10. Class Exercise • Exercise 19. (p. 718) • Each pair of students should use only one sheet of paper while solving the class exercises

More Related