1 / 16

Computer Science 101

Computer Science 101. Logic Circuits. From Boolean Logic to Hardware. Boolean values true and false map to binary values 1 and 0 Binary values 1 and 0 map to discrete states on and off Discrete states on and off map to voltage levels +5V and 0V on an analog device

ishmael-dawson
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 Circuits

  2. From Boolean Logic to Hardware • Boolean values true and false map to binary values 1 and 0 • Binary values 1 and 0 map to discrete states on and off • Discrete states on and off map to voltage levels +5V and 0V on an analog device • Connect these devices to perform logical operations

  3. Collector Base Switch Emitter Transistor - Electronic Switch • Base High (+5v or 1) Makes connection • Base Low (0v or 0) Disconnects

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

  5. +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

  6. NOT Gate _ A A NOT Gate +5v • 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 Output Input Ground

  7. 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.

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

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

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

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

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

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

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

  15. 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 to label 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.

  16. The Boolean Triangle Boolean Expression Logic Circuit Truth Table

More Related