Comparator Between A,B,C ? Check my answer PLS

[IronMan2010]

So the Problem says : Three Inputs A,B,C are three,Four and Five bits respictively, Write the expression that gives one logic output only when ( A=c<B ).

My Answer : ( A=c< B ) = [C4'.C3'.Xa2.Xa1.Xa0][B2.C2'+Xb2.B1.C1'+Xb2.Xb1.B0.C0']

where Xa= AC + A'B'
and
Xb= BC + B'C'


Am I right ??

 

[MikeMl]

Since C has 5 bits, C<B only when the m.s.b. of C (C4) is zero AND (the four rightmost bits of C are less than the four bits of B).

Doesn't that require a four-bit magnitude comparator followed by an AND gate to reduce that to a single bit output.

Further; a single XNOR will test that A is equal to that single output from the above.

 

[IronMan2010]

SO i make AND between C4' & B>C out of comparator , ok i get that to make sure B>C, But I dont get the XNOR part ??

 

[MikeMl]

Prove that for 4 bit numbers, if B>C then it follows that C<B.

Define a one-bit variable X such that X = (C<B)

Now generate a one-bit output Y such that A=X. What logic does this?

 

[IronMan2010]

Sorry Dont get how XNOR between A three bits and X one bit will satsify my desired output A=C<B ?

 

[MikeMl]

Sorry Dont get how XNOR between A three bits and X one bit will satsify my desired output A=C<B ?

I may have confused you. I went back and reread the statement of the problem, and now I don't understand it?

What does A=B<C mean?

Does that mean that a single bit output (call it Y) is true if (A==B) AND (B>C)? [using equality == and relational > as in C].

My confusion is because A = (B<C) has a totally different meaning. It cant be this usage because the problem statement says that A is a 3 bit variable.

 

[IronMan2010]

The statement IS A=C and C < B and i need Expression that gives logic 1 when this is verified "A=C" amd ""C < B"" , I dont know why you didnt check My Answer at post #1 ? And thank you for HelP, your effort is appreciated man.. I have an Exam On Combinational Circuits and sequential circuits Nxt Sunday

 

[IronMan2010]

The statement IS A=C and C < B and i need Expression that gives logic 1 when this is verified "A=C" amd ""C < B"" , I dont know why you didnt check My Answer at post #1 ? And thank you for HelP, your effort is appreciated man.. I have an Exam On Combinational Circuits and sequential circuits Nxt Sunday