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EE2420 – Digital LogicSummer 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!
- 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

- 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

- 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 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

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 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

- 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

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.

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)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 = (XY)’ = X’Y’ + XY

XNOR (Equivalence)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

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

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

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

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