On Wed, 17 Oct 2001, Bernard Ebinu wrote:
> Hi Dr. Amaral,
>
> Using what you said in your response, if I was to try to implement an
> 8-to1 mux with a given function
>
> F(X,Y,Z,T) = XY' + Z'T
>
> then I would first expand the function into its full terms.
>
> F(X,Y,Z,T) = XY'Z1 + XY'Z'T + XYZ'T + XYZ'T + X'Y'Z'T + X'YZ'T
>
> correct???
>
> Given I know this informatin I would then assign values to my mux which
> would result in this ouptut. Given that have selected X,Y,Z as my control
> inputs into my mux.
>
> X Y Z OUT
> -------------------------
> 0 0 0 0
> 0 0 1 0
> 0 1 0 T
> 0 1 1 0
> 0 1 1 0
> 1 0 0 T
> 1 0 1 1
> 1 1 0 T
> 1 1 1 T
>
>
> Is what I have done considered implementing the given function in terms of
> a mux?
Bernard, you are in the right path, what you have to do is to expand the
function so that you have X, Y, Z appearing in all the terms of the
function, which you did. For reference, here is my expansion:
F(X,Y,Z,T) = XY' + Z'T
= XY'(Z' + Z) + (X' + X)(Y' + Y)Z'T
= XY'(Z' + Z) + (X'Y' + X'Y + XY' + XY)Z'T
= XY'Z' + XY'Z + X'Y'Z'T + X'YZ'T + XY'Z'T + XYZ'T
= XY'Z' + XY'Z + X'Y'Z'T + X'YZ'T + XYZ'T
= XY'Z'.1 + XY'Z.1 + X'Y'Z'.T + X'YZ'.T + XYZ'.T + X'Y'Z.0 + X'YZ.0 + XYZ.0
= X'Y'Z'.T + X'Y'Z.0 + X'YZ'.T + X'YZ.0 + XY'Z'.1 + XY'Z.1 + XYZ'.T + XYZ.0
PS: of course you can use shortcuts, I am just trying to be complete so
that you can follow each step. Notice that I use a dot notation to
emphasize the separation between the control inputs and the data inputs
for the mux. Now if I generate a table like yours above (from my
derivation), I obtain:
X Y Z OUT
-------------------------
0 0 0 T
0 0 1 0
0 1 0 T
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 T
1 1 1 0
> If so, then I understand your respons, if not I didn't fully
> understand the last e-mail you sent.
These are good questions. Let me know if you understand it better now.
Cheers,
Nelson
/
\ / / Jose Nelson Amaral - amaral@cs.ualberta.ca
) / ( Associate Professor
/ / \ Dept. of Computing Science - University of Alberta
( / ) Edmonton, Alberta, Canada, T6G 2E8
\ O / Phone: (780)492-5411 Fax: (780)492-1071
\ / http://www.cs.ualberta.ca/~amaral
`----'
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