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Digital Electronics
NUMBER SYSTEM
BINARY CODES
BOOLEAN ALGEBRA
BINARY LOGIC
LOGIC GATES
BOOLEAN ALGEBRA LAWS
CONSENSUS THEOREM
DIFFERENT FORS OF BOOLEAN EQUATIONS
RELATION B/W MAX & MIN TERMS
16 type of LOGIC FUNCTIONS
AND & OR GATE
Other GATES
XOR & XNOR gates
NEGATED & COMPLIMENTRY GATES
TRISTATE gates & DIP
Illustration of NEGATIVE & POSITIVE LOGIC
Relation B/W XOR & XNOR gates
UNIVERSAL GATES
Implementation of XOR using minimum gates
Implementation of XNOR using minimum gates
Different levels of CIRCUIT
Special Characteristics of an IC
QUESTIONS
Q1 (Timing Diagram)
Q2 (Timing Diagram)
Q3 (Timing Diagram - DIfferent units)
Q4 (Timing Diagram)
Q5 (Output of Series of NOR gate )
Q6 (Output of combination of XOR )
Q7 (Circuit of NAND gates & diff delays)
K MAPS
COMBINATIONAL CKT
SEQUENTIAL CIRCUITS
TIMING CIRCUITS

 

 

Logical functions:

There can be total of 2 raise to the power 2n functions possible for n binary variables. So for n=2 i.e. two variables we have total of 16 functions and we have already talked about few of those like AND, OR, NOT. So there are 13 more functions to be defined.

F0=0

F1=xy

F2=xy’

F3=x

F4=x’y

F5=y

F6=x’y+xy’

F7=x+y

F8=(x+y)’

F9=xy+x’y’

F10=y’

F11=x+y’

F12=x’

F13=x’+y

F14=(xy)’

F15=0

Out of these 16 functions, 2 are constants F0 &F15

And 4 functions are repeated twice: F2 &F4, F10 &F12, F11 &F13, and F3 &F5

Now we are left with 10 functions and out of these 10 are not commutative and associative hence not practical to use. So in the end we are left with 8 logic functions which are actually the 8 standard gates which are AND, OR, NOT, BUFFER, XOR, X-NOR, NOR, NAND and defined as follow:

All the gates can be extended to multi input gate but there is a limit on the extension of number of inputs which is known as fan-in discussed later. All the 8 gates are commutative and associative.

 


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