mux DIGITAL LOGIC

Question

how to differentiate between these two MUX output?

HOW to decide which of the A, B ,C will be MSB and LSB?

getting confused.!!!

Answer 1

Output at MUX is valid if E = 0 only. then

Output of a MUX = S'₁.S'₀.I₀ + S'₁.S₀.I₁ + S₁.S'₀.I₂ + S₁.S₀.I₃

 = B'.A'.I₀ + B'.A.I₁ + B.A'.I₂ + B.A.I₃

= B'.A'.C + B'.A.C' + B.A'.1 + B.A.C'

= B'.A'.C + B'.A.C' + B.A'.( C + C' ) + B.A.C'

= B'.A'.C + B'.A.C' + B.A'.C + B.A'.C' + B.A.C'

 

if the Function is F(A,B,C), then

F(A,B,C) = B'.A'.C + B'.A.C' + B.A'.C + B.A'.C' + B.A.C'

F(A,B,C) = A'.B'.C + A.B'.C' + A'.B.C + A'.B.C' + A.B.C' = ∑m(001,100,011,010,110) = ∑m(1,4,3,2,6) = ∑m(1,2,3,4,6).

 

if the Function is F(C,B,A), then

F(A,B,C) = B'.A'.C + B'.A.C' + B.A'.C + B.A'.C' + B.A.C'

F(A,B,C) = C.B'.A' + C'.B'.A + C.B.A' + C'.B.A' + C'.B.A = ∑m(100,001,110,010,011) = ∑m(4,1,6,2,3) = ∑m(1,2,3,4,6).

 

in this case, F(A,B,C) = F(C,B,A), but in general may those are not equivalent.

ex :- if the function leads to F = ABC' + A B C

then F(A,B,C) = ∑m(110,111) = ∑m(4,7)

but F(C,B,A) = ∑m(011,111) = ∑m(3,7).

Comments

is it just a matter of expressing things if you replace A & C then both are same  . Is it?

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is it just a matter of expressing things if you replace A & C then both are same  

yes !

Final answer is same, but representation of minterms are different ( may some times those are equal ) !

if a minterm 1, in F(A,B,C) will represent, A' . B' . C

it is equal to minterm 4, in F(C,B,A) will represent, C. B' . A' = A' . B' . C

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ok thanks a lot :)