1 / 25

Computer Science 101

Computer Science 101 . Logic Gates and Simple Circuits. Collector. Base. Switch. Emitter. Transistor - Electronic Switch. Base High (+5v or 1) Makes connection Base Low (0v or 0) Disconnects Say, 500 million transistors on a chip 1 cm 2 Change states in billionth of sec

avedis
Download Presentation

Computer Science 101

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. Computer Science 101 Logic Gates and Simple Circuits

  2. Collector Base Switch Emitter Transistor - Electronic Switch • Base High (+5v or 1) Makes connection • Base Low (0v or 0) Disconnects • Say, 500 million transistors on a chip 1 cm2 • Change states in billionth of sec • Solid state

  3. Moore’s Law In 1965, Intel co-founder Gordon Moore saw the future. His prediction, now popularly known as Moore's Law, states that the number of transistors on a chip doubles about every two years.

  4. Gates • A gateis an electronic device that takes 0/1 inputs and produces a 0/1 result.

  5. NOT Gate _ A A NOT Gate • Input High (+5v or 1) Output Low (0v or 0) • Input Low (0v or 0) Output High (+5v or 1) • Output is opposite of Input +5v Output Input Ground

  6. Input-1 Input-2 AND Gate A B AB AND Gate • Output is 1 only if • Input-1 is 1 and • Input-2 is 1 • Output = Input1 AND Input2 +5v Output

  7. +5v A B Output OR Gate A B A + B OR Gate • Output is 1 if • A is 1 or if • B is 1 • Output = A OR B

  8. Boolean Expression  Python • Logical operators • AND  and (Python) • OR  or (Python) • NOT  not (Python) • NOT ((x>y) AND ((x=5) OR (y=3)) • not((x>y) and ((x==5)or(y==3))) • while (not((x>y) and ((x==5)or(y==3)))) :…

  9. Abstraction • In computer science, the term abstraction refers to the practice of defining and using objects or systems based on the high level functions they provide. • We suppress the fine details of how these functions are carried out or implemented. • In this way, we are able to focus on the big picture. • If the implementation changes, our high level work is not affected.

  10. Abstraction Examples • Boolean algebra - we can work with the Boolean expressions knowing only the properties or laws - we do not need to know the details of what the variables represent. • Gates - we can work with the logic gates knowing only their function (output is 1 only if inputs are …). Don’t have to know how gate is constructed from transistors.

  11. Boolean Exp  Logic Circuit • To draw a circuit from a Boolean expression: • From the left, make an input line for each variable. • Next, put a NOT gate in for each variable that appears negated in the expression. • Still working from left to right, build up circuits for the subexpressions, from simple to complex.

  12. Logic Circuit: _ ____ AB+(A+B)B Input Lines for Variables A B

  13. Logic Circuit: _ ____ AB+(A+B)B NOT Gate for B A B _ B

  14. Logic Circuit: _ ____ AB+(A+B)B _ Subexpression AB _ AB A B _ B

  15. Logic Circuit: _ ____ AB+(A+B)B Subexpression A+B _ AB A A+B B _ B

  16. Logic Circuit: _ ____ AB+(A+B)B ___ Subexpression A+B _ AB A ____ A+B A+B B _ B

  17. Logic Circuit: _ ____ AB+(A+B)B ___ Subexpression (A+B)B _ AB A ____ A+B A+B B _ B ____ (A+B)B

  18. _ AB A ____ A+B A+B B _ B ____ (A+B)B Logic Circuit: _ ____ AB+(A+B)B Entire Expression

  19. Logic Circuit  Boolean Exp • In the opposite direction, given a logic circuit, we can write a Boolean expression for the circuit. • First we label each input line as a variable. • Then we move from the inputs labeling the outputs from the gates. • As soon as the input lines to a gate are labeled, we can label the output line. • The label on the circuit output is the result.

  20. A _ AB _ A ______ _ _ AB+AB B _ AB _ B A+B ______ _ _ (AB+AB)(A+B) Entire Expression Logic Circuit  Boolean Exp _ _ AB+AB

  21. Simplification Revisited • Once we have the BE for the circuit, perhaps we can simplify.

  22. Logic Circuit  Boolean Exp Reduces to:

  23. The Boolean Triangle Boolean Expression Logic Circuit Truth Table

  24. The Boolean Triangle Boolean Expression Logic Circuit Truth Table

  25. If we only had an Al Gore Rhythm!

More Related