digital logic

Question

which is correct?

S1    +ve logic AND operation behaves as -ve logic OR operation.

S2    fxn f(A,B,C)= AB+BC+CA is a self dual fxn.

 

S2 is true but what is the explanation of S1, what does statement 1 want to say?

Comments

In positive logic: high voltage is logic 1, low voltage is logic 0

In negative logic: high voltage is logic 0, low voltage is logic 1

Now try to think about this.

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so according to this definition s1 is false?

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Why?

Consider positive logic:

a	b	a.b
0	0	0
0	1	0
1	0	0
1	1	1

 

a	b	a+b
0	0	0
0	1	1
1	0	1
1	1	1

Complement OR truth table we will get negative logic OR operation

a	b	a+b
1	1	1
1	0	0
0	1	0
0	0	0

This truth table is same as positive logic AND operation 
So S1 is true.

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got it..thanks

m last step me mistake kr ra tha..

Answer 1

AND Gate Truth Table :

A	B	A.B
High	High	High
High	Low	Low
Low	High	Low
Low	Low	Low

 

This table interpreted in +ive logic gives:

       High → 1 and Low → 0

A	B	A.B
1	1	1
1	0	0
0	1	0
0	0	0

 

 

If the 1^st table is interpreted in -ive logic then:

      High → 0 and Low → 1

A	B	A.B
0	0	0
0	1	1
1	0	1
1	1	1

 

 

In above table A.B is 0 only when A and B both are 0 which is property of OR gate. Hence from above table we can conclude that AND gate in -ive logic system acts as OR gate.