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                                                                     EXHIBIT 8.1

                        [COOLEY GODWARD LLP LETTERHEAD]


April 12, 2001


LSI Logic Corporation
1551 McCarthy Boulevard
Milpitas, CA  95035

Ladies and Gentlemen:

This opinion is being delivered to you in connection with the Form S-4
Registration Statement (the "Registration Statement") filed in connection with
(i) the exchange offer (the "Offer") proposed to be made by LSI Logic
Corporation, a Delaware corporation ("Parent"), through its wholly-owned
subsidiary, Clover Acquisition Corp., a Delaware corporation ("Merger Sub"), to
exchange shares of Parent for shares of C-Cube Microsystems Inc., a Delaware
corporation (the "Company"), and (ii) the proposed merger of Merger Sub with and
into the Company (the "Merger"), in each case pursuant to the Agreement and Plan
of Reorganization dated as of March 26, 2001 (the "Reorganization Agreement"),
by and among Parent, Merger Sub, and the Company. Except as otherwise provided,
capitalized terms used but not defined herein shall have the meanings set forth
in the Reorganization Agreement.

We have acted as counsel to Parent in connection with the Offer and the Merger.
As such, and for the purpose of rendering this opinion, we have examined, and
are relying upon (without any independent investigation or review thereof) the
truth and accuracy, at all relevant times, of the statements, covenants,
representations and warranties contained in the following documents (including
all exhibits and schedules attached thereto):

     (a)  the Reorganization Agreement;

     (b)  the Registration Statement, which includes the Preliminary Prospectus
of Parent (the "Preliminary Prospectus");

     (c)  those certain tax representation letters of even date herewith
delivered to us by Parent, Merger Sub and the Company (the "Tax Representation
Letters"); and

     (d)  such other instruments and documents related to the formation,
organization and operation of Parent, Merger Sub and the Company and to the
consummation of the Offer and the Merger and the other transactions contemplated
by the Reorganization Agreement as we have deemed necessary or appropriate.

In connection with rendering this opinion, we have assumed (without any
independent investigation or review thereof) that:

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LSI Logic Corporation
April 12, 2001
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     (a)  Original documents submitted to us (including signatures thereto) are
authentic, documents submitted to us as copies conform to the original
documents, and that all such documents have been (or will be by the closing of
the Offer or the Effective Time of the Merger, as the case may be) duly and
validly executed and delivered where due execution and delivery are a
prerequisite to the effectiveness thereof;

     (b)  All representations, warranties and statements made or agreed to by
Parent, Merger Sub and the Company, their managements, employees, officers,
directors and stockholders in connection with the Offer and the Merger,
including, but not limited to, those set forth in the Reorganization Agreement
(including the exhibits thereto) and the Tax Representation Letters are true and
accurate at all relevant times and any representation or statement made "to the
knowledge of" or similarly qualified is correct without such qualification;

     (c)  All covenants contained in the Reorganization Agreement (including
exhibits thereto) and the Tax Representation Letters are performed without
waiver or breach of any material provision thereof; and

     (d)  The opinion of even date herewith rendered by Wilson Sonsini Goodrich
& Rosati, P.C., to the Company and filed as Exhibit 8.2 to the Registration
Statement has been delivered and has not been withdrawn.

Based on our examination of the foregoing items and subject to the limitations,
qualifications, assumptions and caveats set forth herein, we believe that the
discussion entitled "Material Federal Income Tax Consequences" contained in the
Preliminary Prospectus, insofar as it relates to statements of law and legal
conclusions, sets forth the material federal income tax considerations generally
applicable to the Offer and the Merger.

This opinion does not address the various state, local or foreign tax
consequences that may result from the Offer and the Merger or the other
transactions contemplated by the Reorganization Agreement. In addition, no
opinion is expressed as to any federal income tax consequence of the Offer or
Merger or the other transactions contemplated by the Reorganization Agreement
except as specifically set forth herein, and this opinion may not be relied upon
except with respect to the consequences specifically discussed herein.

No opinion is expressed as to any transaction other than the Offer and the
Merger as described in the Reorganization Agreement, or as to any transaction
whatsoever, including the Offer and the Merger, if any of the representations,
warranties, statements and assumptions material to our opinion and upon which we
have relied are not accurate and complete in all material respects at all
relevant times.

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[COOLEY GODWARD LLP LETTERHEAD]

LSI Logic Corporation
April 12, 2001
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This opinion only represents our best judgment as to the federal income tax
consequences of the Offer and the Merger and is not binding on the Internal
Revenue Service or any court of law, tribunal, administrative agency or other
governmental body. The conclusions are based on the Internal Revenue Code of
1986, as amended, existing judicial decisions, administrative regulations and
published rulings. Because this opinion is being delivered prior to the
Effective Time of the Merger, it must be considered prospective and dependent on
future events. No assurance can be given that future legislative, judicial or
administrative changes or interpretations would not adversely affect the
accuracy of the conclusions stated herein. Nevertheless, by rendering this
opinion, we undertake no responsibility to advise you of any new developments in
the application or interpretation of the federal income tax laws.

This opinion is being delivered solely in connection with the filing of the
Registration Statement. It is intended for the benefit of Parent and may not be
relied upon or utilized for any other purpose or by any other person and may not
be made available to any other person without our prior written consent.

We consent to the reference to our firm under the caption "Material Federal
Income Tax Consequences" in the Preliminary Prospectus and to the reproduction
and filing of this opinion as an exhibit to the Registration Statement.

Sincerely,


COOLEY GODWARD LLP

/s/ Webb B. Morrow III
-----------------------
Webb B. Morrow III

RHM:ls