﻿ Boolean Algebra - DUALITY Principle, Huntington Postulates and THEOREMS. Commutative , distributive property.        Custom Search Chip Designing for ASIC/ FPGA Design engineers and Students
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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’.

Digital Logic fundamentals topics @ fcd. Digital basics tutorial
Binary number discussion, 1 and 2 complement discussion, Binary arithmetic, Signed Magnitude, overflow, examples, Gray coding, Binary coded digital (BCD) coding, BCD addition
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Discussion of Boolean Algebra with examples.
Duality Principle, Huntington Postulates, Theorems of Boolean Algebra - discussion with examples, 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  Resources
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1. F(x,y,z) =     (0,1,6,7) - Minimization, on this page.
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