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Binary Numbers 1s_complement 2s_complement Binary Subtraction Binary Sub. Ex's Sign_magnitude SignM EX Gray Coding BCD coding Digital gates NAND NOR & XNOR Theorems Boolean Functions BFunc Examples Minterm Maxterm Sum of Minterms Prdt of Maxterms 2 var K-map 3 var K-map 4 var K-map 5 var K-map Prime Implicant PI example K-map Ex's KMap minimization 2 var EX

Boolean Algebra

 

Duality Principle:

The duality property of Boolean algebra state that all binary expressions remain valid when following two steps are performed:

Step 1 :  Interchange OR and AND operators.

Step 2 :  Replace all 1’s by 0’s and 0’s by 1’s.

Huntington Postulates

Adding a number to ‘0’ :

P1. Postulate:- x + 0 = x, next From duality of P1

 

P2. Postulate:- x * 1 = x

Sum of a number and its complement from a Set is ‘1’.

 

Top Tech Topics @FCD
K-map - 2,3,4,5 var & Prime Implicant discussion
Verilog - learn with examples
Interview questions and hints

P3. Postulate:- x + x’= 1, next From duality of P3

 

P4. Postulate:- x * x’ = 0

From commutative property of binary numbers we have:-

 

P5. Postulate:- x + y = y + x

From duality of P5

 

P6. Postulate:- x * y = y * x

From distributive property of binary numbers we have:-

 

P7. Postulate:- x(y + z) = xy + xz

From duality of P7

NAND NOR & XNOR.Boolean Functions.
Solved Examples for 3 variable Kmaps
1. F(x,y,z) =     (0,1,6,7) - Minimization, on this page.
2. F(x,y,z) =     (0,1,4,5,6,7) - Minimization from here.
3. F(x,y,z) =     (3,4,6,7) - Minimization from here.
4. F(x,y,z) =     (0,1,2,3,4,5,6,7) - Minimization from here.

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