A Digital Logic Question

[magnetra]

logic question tagalog

Let A and B both be binary logic variables.
Then
A + A•B
= A(1 + B)
= A•1
= A.

Does this imply that A•B = 0 ?

M

 

[ahmed_nasr]

digital logic simplification a + ab

of course not .... because this is a logic operation not an arithmetic operation ... so the result means that A+A.B is independent of B but depends only on the variable A

 

[neils_arm_strong]

What about A.(A+B)=A
this means A+B=1 so from X+X'=1 can't we say B=A'.
Then A.B=A.B'=0.
Correct me if i am wrong.

 

[Naveed Alam]

Let A and B both be binary logic variables.
Then
A + A•B
= A(1 + B)
= A•1
= A.

Does this imply that A•B = 0 ?

M

no, it means ur output status will be the status of input A.

 

[amriths04]

LET A=1 AND B=1
A+B=1
THUS, IS A+B=A OR IS A+B=B??

in this case it does not matter whether the output is A or B.

similarly,in your case, the output does not depend on B. whatever change you make to B the output will remain constant (unless and untill you change A).

regards,

 

[magnetra]

Let A and B both be binary logic variables.
Then
A + A•B
= A(1 + B)
= A•1
= A.

of course not .... because this is a logic operation not an arithmetic operation ... so the result means that A+A.B is independent of B but depends only on the variable A

If A and B were two binary sequences of length N, then can I say that A and B are orthogonal to each other?

M

 

[magnetra]

Please, anyone, any comment????????

 

[white_shadow]

Let A and B both be binary logic variables.
Then
A + A•B
= A(1 + B)
= A•1
= A.

Does this imply that A•B = 0 ?

M

A B A and B A or (A and B)
0 0 0 0
0 1 0 0
1 0 0 1
1 1 1 1

Does this clarify things for you. You seem to be confused with the arithmetic use of "+" versus the logic use which means "or".

 

[amriths04]

orthogonality is ascosciated only with vectors i suppose. A.B does not mean the dot product of 2 vectors. the . is a logical operator.

If A and B were two binary sequences of length N, then can I say that A and B are orthogonal to each other?
M

 

[magnetra]

Can't we show that two binary sequences are orthogonal? I found this material (pic). This pic is from 'Technical Introduction to CDMA' by Scott Baxter.

M

 

[Electronica]

Cant cuz the OR operation implies that the o/p would depend on A

 

[vinod_g]

see A+A.B means A.B =0 means A =0 r B=0 then the result depends on A means A=1 or 0,if A.B=1 means automatically A=1,result also 1.so it defines that result depends om A

 

[vijaiiyer]

The boolean arithmetic can be easily used for confusion. The stress here is on 'boolean' and not 'arithmetic'. All the evaluation results only in simplification of logic, giving the results as to On what logic values the output is dependednt on.. and does not imply anything on the individual values.

 

[sivakumar_tumma]

NO it is not... what u said will work for naormal algebra ... not for this...