1 / 20

EE2420 – Digital Logic Summer II 2013

EE2420 – Digital Logic Summer II 2013. Set 4: Other Gates. Hassan Salamy Ingram School of Engineering Texas State University. Other Logic Gates. NOT NAND – Not AND NOR - Not OR XOR - Exclusive OR XNOR - Equivalence function (X  Y). NOT. Not AND - Easy to build – only 2 gates!

iden
Download Presentation

EE2420 – Digital Logic Summer II 2013

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. EE2420 – Digital LogicSummer II 2013 Set 4: Other Gates Hassan Salamy Ingram School of Engineering Texas State University

  2. Other Logic Gates • NOT • NAND – Not AND • NOR - Not OR • XOR - Exclusive OR • XNOR - Equivalence function (X  Y)

  3. NOT • Not AND - Easy to build – only 2 gates! • http://tams-www.informatik.uni-hamburg.de/applets/cmos/index.html

  4. NAND • Not AND - Easier to build than AND – only 4 gates! • http://tams-www.informatik.uni-hamburg.de/applets/cmos/index.html

  5. NOR • Not OR

  6. Design examples • Logic circuits provide a solution to a problem • Some may be complex and difficult to design • Regardless of the complexity, the same basic design issues must be addressed • Specify the desired behavior of the circuit • Synthesize and implement the circuit • Test and verify the circuit

  7. Multiplexer circuit • In computer systems it is often necessary to choose data from exactly one of a number of sources • Design a circuit that has an output (f) that is exactly the same as one of two data inputs (x,y) based on the value of a control input (s) • If s=0 then f=x • If s=1 then f=y • The function f is really a function of three variables (s,x,y) • Describe the function in a three variable truth table

  8. Multiplexer circuit f(s,x,y)=m2+m3+m5+m7 f(s,x,y)=s’xy’+s’xy+sx’y+sxy f(s,x,y)=s’x(y’+y)+sy(x’+x) f(s,x,y)=s’x+sy convenient to put control signal on left

  9. s x1 0 1 x2 Multiplexer circuit f=x1s’+x2s Graphical symbol Compact truth table

  10. Car safety alarm • Design a car safety alarm considering four inputs • Door closed (D) • Key in (K) • Seat pressure (S) • Seat belt closed (B) • The alarm (A) should sound if • The key is in and the door is not closed, or • The door is closed and the key is in and the driver is in the seat and the seat belt is not closed

  11. Car safety alarm A(D,K,S,B)=Sm(4,5,6,7,14) A(D,K,S,B)=D’KS’B’+D’KS’B+D’KSB’+D’KSB+DKSB’ =D’KS’+D’KS+KSB’ =D’K+KSB’

  12. XOR - Three-way light control • Assume a room has three doors and a switch by each door controls a single light in the room. • Let x, y, and z denote the state of the switches • Assume the light is off if all switches are open • Closing any switch turns the light on. Closing another switch will have to turn the light off. • Light is on if any one switch is closed and off if two (or no) switches are closed. • Light is on if all three switches are closed Lecture 4: Other Logic Gates

  13. Three-way light control f(x,y,z)=m1+m2+m4+m7 f(x,y,z)=x’y’z+x’yz’+xy’z’+xyz This is the simplest sum-of-products form.

  14. The Boolean function OR is more correctly called the Inclusive-OR The Exclusive-Or, abbreviated XOR with the symbol , operates in the following manner: X  Y is true if X is true exclusively or if Y is true exclusively but is false if both X and Y are true X  Y = X’Y + XY’ Exclusive-OR (XOR)

  15. The inverse to XOR is XNOR. XNOR is sometimes listed as the Equivalence function (X  Y) XNOR/Equivalence is true if both inputs are false or if both inputs are true X  Y = (XY)’ = X’Y’ + XY XNOR (Equivalence)

  16. XOR and XNOR circuit symbols • The XOR symbol is similar to the OR symbol with the addition of the additional input bar. • The XNOR symbol is equivalent to the XOR symbol with the addition of the inversion circle at the output. XOR XNOR Lecture 4: Other Logic Gates

  17. Adder circuit • Design a circuit that adds two input bits together (x,y) and produces two output bits (s and c) • S: sum bit • x=0, y=0 => s=0 • x=0, y=1 => s=1 • x=1, y=0 => s=1 • x=1, y=1 => s=0 • C: carry bit • x=0, y=0 => c=0 • x=0, y=1 => c=0 • x=1, y=0 => c=0 • x=1, y=1 => c=1

  18. C = XY S = X’Y + XY’ = X  Y Adder Circuit

  19. Majority circuit • Design a circuit with three inputs (x,y,z) whose output (f) is 1 only if a majority of the inputs are 1 • Construct a truth table • Write a standard sum-of-products expression for f • Draw a circuit diagram for the sum-of-products expression • Minimize the function using algebraic manipulation • During your minimization you can use any Boolean theorem, but leave the result in sum-of-products form (generate a minimum sum-of-products expression) • Draw the minimized circuit

  20. Majority Function • The output of the majority function is equal to the value for the three inputs which occurs on more inputs. • Majority(X,Y,Z) = m(3,5,6,7) • Majority(X,Y,Z) = X’YZ + XY’Z + XYZ’ + XYZ • Simplified  Majority(X,Y,Z) = XY + XZ + YZ

More Related