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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!

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Ee2420 digital logic summer ii 2013
EE2420 – Digital LogicSummer II 2013

Set 4: Other Gates

Hassan Salamy

Ingram School of Engineering

Texas State University


Other logic gates
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!

  • http://tams-www.informatik.uni-hamburg.de/applets/cmos/index.html


NAND

  • Not AND - Easier to build than AND – only 4 gates!

  • http://tams-www.informatik.uni-hamburg.de/applets/cmos/index.html


NOR

  • Not OR


Design examples
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


Multiplexer circuit
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


Multiplexer circuit1
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


Multiplexer circuit2

s

x1

0

1

x2

Multiplexer circuit

f=x1s’+x2s

Graphical symbol

Compact truth table


Car safety alarm
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


Car safety alarm1
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’


Xor three way light control
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


Three way light control
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.


Exclusive or xor

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)


Xnor equivalence

The inverse to XOR is XNOR. Inclusive-OR

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)


Xor and xnor circuit symbols
XOR and XNOR circuit symbols Inclusive-OR

  • 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


Adder circuit
Adder circuit Inclusive-OR

  • 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


Adder circuit1

C = XY Inclusive-OR

S = X’Y + XY’ = X  Y

Adder Circuit


Majority circuit
Majority circuit Inclusive-OR

  • 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


Majority function
Majority Function Inclusive-OR

  • 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


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