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

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

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

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

5. NOR  Not OR 5

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 1. Specify the desired behavior of the circuit 2. Synthesize and implement the circuit 3. Test and verify the circuit 6

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 7

8. Multiplexer circuit sxyf 0000 0010 0101 0111 1000 1011 1100 1111 f(s,x,y)=m 2 +m 3 +m 5 +m 7 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 8

9. Multiplexer circuit 0 1 s x1x1 x2x2 f=x 1 s’+x 2 s sf(s,x 1,x 2 ) 0x1x1 1x2x2 Graphical symbolCompact truth table 9

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 10

11. Car safety alarm DKSBA 00000 00010 00100 00110 01001 01011 01101 01111 10000 10010 10100 10110 11000 11010 11101 11110 A(D,K,S,B)=m(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’ 11

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 12

13. Three-way light control xyzf 0000 0011 0101 0110 1001 1010 1100 1111 f(x,y,z)=m 1 +m 2 +m 4 +m 7 f(x,y,z)=x’y’z+x’yz’+xy’z’+xyz This is the simplest sum-of-products form. 13

14. Exclusive-OR (XOR) XY XYXY 000 011 101 110  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’ 14

15. XNOR (Equivalence) XY XYXY(X  Y) Same as (XY)’ 0001 0110 1010 1101  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 15

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 16

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 17

18. Adder Circuit 18 XYC (carry) S (sum) 0000 0101 1001 1110  C = XY  S = X’Y + XY’ = X  Y

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 19

20. Majority Function 20 XYZMajority 0000 0010 0100 0111 1000 1011 1101 1111 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