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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

 

 

Consensus theorem:

Given a pair of terms for which a variable appears in one term and its compliment in the other term then consensus term is formed by ANDing the original terms together leaving out the selected variable and its compliment.

 

e.g.        Find consensus term out of the two terms X.Y & X’.Z

                Consensus term is Y.Z

e.g.        Find consensus term out of the two terms  XYZ & Y’ZW’

Consensus term is (XZ). (ZW’)

 

SO X is left and simplified expression is XY’ + Y

And apply elimination law we get answer as X + Y

 

Or apply distributive law so we get (X + Y) (Y’ + Y)

And Y + Y’ = 1 hence we get simplified answer as X + Y

 

Leaving the consensus term from expression and we get the result as (X +Y) (X’+ Z)

Min term: All the combinations of the n variable to form 2 n AND terms are called MIN TERMs or standard products. For n=2 and variables x & y we have min terms as xy, xy’, x’y, x’y’ and similarly for n=3 and variables x, y, z we have the min terms as xyz, xyz’, x’yz, xy’z, x’y’z, x’yz’, xy’z’, x’y’z’. Min term is generally represented by letter ‘m’ (lower case) and to distinguish between different min terms we place a subscript with m and suffix is decided for a particular term by following procedure:

 

We put a 0 for the literal with compliment (‘) and a 1 for the literal without compliment and then take its binary equivalent. Decimal we get is placed as a subscript as shown below

 

xyz = 111 = 7 so min term is m7                   x’yz’ = 010 = 2    m2                       xyz’ = 110 = 6   m6 etc

 

Max terms: similarly all the combinations of the n variable to form 2 n OR terms are called MAX TERMs or standard sums. For n=2 and variables x & y we have max terms as x+y, x+y’, x’+y, x’+y’ and similarly for n=3 and variables x, y, z we have the max terms as x+y+z, x+y+z’, x’+y+z, x+y’+z, x’+y’+z, x’+y+z’, x+y’+z’, x’+y’+z’. Max term is represented by ‘M’ (capital) and procedure to find the subscript is exact opposite.

 

We put a 1 for the literal with compliment (‘) and a 0 for the literal without compliment and then take its binary equivalent. Decimal we get is placed as a subscript as shown below

 

x+y’+z= 010 = 2 max term is M2                          x’+y+z =100 = 4 M4                                    x’+y’+z’=111=7  M7

 


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