DeMorgan' Laws

E.g.1

De Morgan's laws are indispensable in digital electronics. The laws outlined by him are simple to understand, yet transformed the Boolean algebra in a dramatic way.

First Law

A + B = A.B

Proof:


BooleanOne

 

Input and Output
A BA+BA + B
1 010
0110
0001
1110
BooleanTwo

 

Input and Output
A BABA.B
10010
01100
00111
11000

Second Law

A.B = A + B


Proof:


BooleanThree
Input and Output
A BA.BA.B
1 001
0101
0001
1110
BooleanFour

 

Input and Output
A BABA + B
10011
01101
00111
11000

Now try the following with a circuit and a truth table:

  1. A + B.C = A.B.C
  2. A + B.C + A.B = A.B
  3. A + AB = A + B
  4. AB + AB = A


 

 

Recommended Reading

 

Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7th edition in print.

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