RESTATED
 
                          CERTIFICATE OF INCORPORATION
 
                                       OF
 
                          ASPECT MEDICAL SYSTEMS, INC.
 
 
         Aspect Medical Systems, Inc., a corporation organized and existing
under and by virtue of the General Corporation Law of the State of Delaware,
does hereby certify as follows:
 
     1.   The Corporation filed its original Certificate of Incorporation with
the Secretary of State of the State of Delaware on October 14, 1987 under the
name "Biometrak Corporation". The Certificate of Incorporation was amended by a
Certificate of Amendment of Certificate of Incorporation filed on February 18,
1988, a Certificate of Amendment of Certificate of Incorporation filed on April
8, 1988, a Certificate of Amendment of Certificate of Incorporation filed on
February 8, 1989, a Certificate of Amendment of Certificate of Incorporation
filed on November 21, 1989, a Certificate of Amendment of Certificate of
Incorporation filed on July 11, 1990, a Certificate of Amendment of Certificate
of Incorporation filed on September 19, 1991, a Certificate of Amendment of
Certificate of Incorporation filed on March 12, 1992, a Certificate of Amendment
of Certificate of Incorporation filed on May 21, 1993 and a Certificate of
Amendment of Certificate of Incorporation filed on August 8, 1994. A Restated
Certificate of Incorporation was filed with the Secretary of State of the State
of
 
 
 
<PAGE>   2
 
 
 
Delaware on November 1, 1995, which Restated Certificate of Incorporation was
amended by a Certificate of Amendment of Restated Certificate of Incorporation
filed on June 27, 1996. A Restated Certificate of Incorporation was filed with
the Secretary of State of the State of Delaware on February 25, 1997. A Restated
Certificate of Incorporation was filed with the Secretary of State of the State
of Delaware on February 13, 1998, which Restated Certificate of Amendment was
amended by a Certificate of Amendment of Restated Certificate of Incorporation
filed on August, 18, 1998. A Restated Certificate of Incorporation was filed
with the Secretary of State of the State of Delaware on December 17, 1998, which
Restated Certificate of Incorporation was amended by a Certificate of Amendment
to the Restated Certificate of Incorporation filed on _____________, 1999.
 
     2.   By vote of the Board of Directors of the Corporation, a resolution was
duly adopted, pursuant to Section 245 of the General Corporation Law of the
State of Delaware, setting forth a Restated Certificate of Incorporation of the
Corporation and declaring said Restated Certificate of Incorporation advisable.
The stockholders of the Corporation duly approved said proposed Restated
Certificate of Incorporation in accordance with Sections 228, 242 and 245 of the
General Corporation Law of the State of Delaware by written consent in lieu of a
special meeting. The resolution setting forth the Restated Certificate of
Incorporation is as follows:
 
RESOLVED:      That the Restated Certificate of Incorporation of the
               Corporation, as amended, be, and hereby is, amended and restated
               in its entirety so that the same shall read as follows:
 
 
 
 
                                       -2-
 
<PAGE>   3
 
 
 
     FIRST.    The name of the Corporation is:
 
                          Aspect Medical Systems, Inc.
 
     SECOND.   The address of the its registered office in the State of Delaware
is Corporation Trust Center, 1209 Orange Street, in the City of Wilmington,
County of New Castle 19801. The name of its registered agent at such address is
The Corporation Trust Company.
 
     THIRD.    The nature of the business or purposes to be conducted or
promoted by the Corporation is as follows:
 
          To engage in any lawful act or activity for which corporations may be
     organized under the General Corporation Law of Delaware.
 
     FOURTH:   The total number of shares of all classes of stock which the
Corporation shall have authority to issue is Sixty Five Million (65,000,000)
shares, consisting of (i) Sixty Million (60,000,000) shares of Common Stock,
$.01 par value per share ("Common Stock"), and (ii) Five Million (5,000,000)
shares of Preferred Stock, $.01 par value per share ("Preferred Stock"), which
may be issued from time to time in one or more series as set forth in Part B of
this Article FOURTH.
 
     The following is a statement of the designations and the powers, privileges
and rights, and the qualifications, limitations or restrictions thereof in
respect of each class of capital stock of the Corporation.
 
A.   COMMON STOCK.
 
     1.   GENERAL. The voting, dividend and liquidation rights of the holders of
the Common Stock are subject to and qualified by the rights of the holders of
the Preferred Stock of any series as may be designated by the Board of Directors
upon any issuance of the Preferred Stock of any series.
 
     2.   VOTING. The holders of the Common Stock are entitled to one vote for
each share held at all meetings of stockholders. There shall be no cumulative
voting.
 
     The number of authorized shares of Common Stock may be increased or
decreased (but not below the number of shares thereof then outstanding) by the
affirmative vote of the holders of a majority of the stock of the Corporation
entitled to vote, irrespective of the provisions of Section 242(b)(2) of the
General Corporation Law of Delaware.
 
 
                                       -3-
 
<PAGE>   4
 
 
     3.   DIVIDENDS. Dividends may be declared and paid on the Common Stock from
funds lawfully available therefor as and when determined by the Board of
Directors and subject to any preferential dividend rights of any then
outstanding Preferred Stock.
 
     4.   LIQUIDATION. Upon the dissolution or liquidation of the Corporation,
whether voluntary or involuntary, holders of Common Stock will be entitled to
receive all assets of the Corporation available for distribution to its
stockholders, subject to any preferential rights of any then outstanding
Preferred Stock.
 
B.   PREFERRED STOCK.
 
     Preferred Stock may be issued from time to time in one or more series, each
of such series to have such terms as stated or expressed herein and in the
resolution or resolutions providing for the issue of such series adopted by the
Board of Directors of the Corporation as hereinafter provided. Any shares of
Preferred Stock which may be redeemed, purchased or acquired by the Corporation
may be reissued except as otherwise provided by law. Different series of
Preferred Stock shall not be construed to constitute different classes of shares
for the purposes of voting by classes unless expressly provided.
 
     Authority is hereby expressly granted to the Board of Directors from time
to time to issue the Preferred Stock in one or more series, and in connection
with the creation of any such series, by resolution or resolutions providing for
the issue of the shares thereof, to determine and fix such voting powers, full
or limited, or no voting powers, and such designations, preferences and relative
participating, optional or other special rights, and qualifications, limitations
or restrictions thereof, including without limitation thereof, dividend rights,
conversion rights, redemption privileges and liquidation preferences, as shall
be stated and expressed in such resolutions, all to the full extent now or
hereafter permitted by the General Corporation Law of Delaware. Without limiting
the generality of the foregoing, the resolutions providing for issuance of any
series of Preferred Stock may provide that such series shall be superior or rank
equally or be junior to the Preferred Stock of any other series to the extent
permitted by law. Except as otherwise provided in this Restated Certificate of
Incorporation, no vote of the holders of the Preferred Stock or Common Stock
shall be a prerequisite to the designation or issuance of any shares of any
series of the Preferred Stock authorized by and complying with the conditions of
this Restated Certificate of Incorporation, the right to have such vote being
expressly waived by all present and future holders of the capital stock of the
Corporation.
 
     FIFTH.    The Corporation shall have a perpetual existence.
 
 
 
                                       -4-
 
<PAGE>   5
 
 
     SIXTH.    In furtherance of and not in limitation of powers conferred by
statute, it is further provided that the Board of Directors is expressly
authorized to adopt, amend or repeal the Amended and Restated Bylaws of the
Corporation (the "Bylaws").
 
     SEVENTH.  Whenever a compromise or arrangement is proposed between this
corporation and its creditors or any class of them and/or between this
corporation and its stockholders or any class of them, any court of equitable
jurisdiction within the State of Delaware may, on the application in a summary
way of this corporation or of any creditor or stockholder thereof, or on the
application of any receiver or receivers appointed for this corporation under
the provisions of section 291 of Title 8 of the Delaware Code or on the
application of trustees in dissolution or of any receiver or receivers appointed
for this corporation under the provisions of section 279 of Title 8 of the
Delaware Code order a meeting of the creditors or class of creditors, and/or of
the stockholders or class of stockholders of this corporation, as the case may
be, to be summoned in such manner as the said court directs. If a majority in
number representing three-fourths in value of the creditors or class of
creditors, and/or of the stockholders or class of stockholders of this
corporation, as the case may be, agree to any compromise or arrangement and to
any promise or arrangement, the said compromise or arrangement and the said
reorganization shall, if sanctioned by the court to which the said application
has been made, be binding on all the creditors or class of creditors, and/or on
all the stockholders or class of stockholders, of this corporation, as the case
may be, and also on this corporation.
 
     EIGHTH.   Except to the extent that the General Corporation Law of the
State of Delaware prohibits the elimination or limitation of liability of
directors for breaches of fiduciary duty, no director of the Corporation shall
be personally liable to the Corporation or its stockholders for monetary damages
for any breach of fiduciary duty as a director, notwithstanding any provision of
law imposing such liability. No amendment to or repeal of this provision shall
apply to or have any effect on the liability or alleged liability of any
director of the Corporation for or with respect to any acts or omissions of such
director occurring prior to such amendment.
 
     NINTH.    1. ACTION, SUITS AND PROCEEDINGS OTHER THAN BY OR IN THE RIGHT OF
THE CORPORATION. The Corporation shall indemnify each person who was or is a
party or is threatened to be made a party to any threatened, pending or
completed action, suit or proceeding, whether civil, criminal, administrative or
investigative (other than an action by or in the right of the Corporation), by
reason of the fact that he is or was, or has agreed to become, a director or
officer of the Corporation, or is or was serving, or has agreed to serve, at the
request of the Corporation, as a director, officer or trustee of, or in a
similar capacity with, another corporation, partnership, joint venture, trust or
 
 
 
                                       -5-
 
<PAGE>   6
 
 
other enterprise (including any employee benefit plan) (all such persons being
referred to hereafter as an "Indemnitee"), or by reason of any action alleged to
have been taken or omitted in such capacity, against all expenses (including
attorneys' fees), judgments, fines and amounts paid in settlement actually and
reasonably incurred by him or on his behalf in connection with such action, suit
or proceeding and any appeal therefrom, if he acted in good faith and in a
manner he reasonably believed to be in, or not opposed to, the best interests of
the Corporation, and, with respect to any criminal action or proceeding, had no
reasonable cause to believe his conduct was unlawful. The termination of any
action, suit or proceeding by judgment, order, settlement, conviction or upon a
plea of NOLO CONTENDERE or its equivalent, shall not, of itself, create a
presumption that the person did not act in good faith and in a manner which he
reasonably believed to be in, or not opposed to, the best interests of the
Corporation, and, with respect to any criminal action or proceeding, had
reasonable cause to believe that his conduct was unlawful. Notwithstanding
anything to the contrary in this Article, except as set forth in Section 6
below, the Corporation shall not indemnify an Indemnitee seeking indemnification
in connection with a proceeding (or part thereof) initiated by the Indemnitee
unless the initiation thereof was approved by the Board of Directors of the
Corporation.
 
     2.   ACTIONS OR SUITS BY OR IN THE RIGHT OF THE CORPORATION. The
Corporation shall indemnify any Indemnitee who was or is a party or is
threatened to be made a party to any threatened, pending or completed action or
suit by or in the right of the Corporation to procure a judgment in its favor by
reason of the fact that he is or was, or has agreed to become, a director or
officer of the Corporation, or is or was serving, or has agreed to serve, at the
request of the Corporation, as a director, officer or trustee of, or in a
similar capacity with, another corporation, partnership, joint venture, trust or
other enterprise (including any employee benefit plan), or by reason of any
action alleged to have been taken or omitted in such capacity, against all
expenses (including attorneys' fees) and amounts paid in settlement actually and
reasonably incurred by him or on his behalf in connection with such action, suit
or proceeding and any appeal therefrom, if he acted in good faith and in a
manner he reasonably believed to be in, or not opposed to, the best interests of
the Corporation, except that no indemnification shall be made in respect of any
claim, issue or matter as to which such person shall have been adjudged to be
liable to the Corporation unless and only to the extent that the Court of
Chancery of Delaware shall determine upon application that, despite the
adjudication of such liability but in view of all the circumstances of the case,
such person is fairly and reasonably entitled to indemnity for such expenses
(including attorneys' fees) which the Court of Chancery of Delaware shall deem
proper.
 
     3.   INDEMNIFICATION FOR EXPENSES OF SUCCESSFUL PARTY. Notwithstanding the
other provisions of this Article, to the extent that an Indemnitee has been
successful, on
 
 
                                       -6-
 
<PAGE>   7
 
 
 
the merits or otherwise, in defense of any action, suit or proceeding referred
to in Sections 1 and 2 of this Article, or in defense of any claim, issue or
matter therein, or on appeal from any such action, suit or proceeding, he shall
be indemnified against all expenses (including attorneys' fees) actually and
reasonably incurred by him or on his behalf in connection therewith. Without
limiting the foregoing, if any action, suit or proceeding is disposed of, on the
merits or otherwise (including a disposition without prejudice), without (i) the
disposition being adverse to the Indemnitee, (ii) an adjudication that the
Indemnitee was liable to the Corporation, (iii) a plea of guilty or NOLO
CONTENDERE by the Indemnitee, (iv) an adjudication that the Indemnitee did not
act in good faith and in a manner he reasonably believed to be in or not opposed
to the best interests of the Corporation, and (v) with respect to any criminal
proceeding, an adjudication that the Indemnitee had reasonable cause to believe
his conduct was unlawful, the Indemnitee shall be considered for the purposes
hereof to have been wholly successful with respect thereto.
 
     4.   NOTIFICATION AND DEFENSE OF CLAIM. As a condition precedent to his
right to be indemnified, the Indemnitee must notify the Corporation in writing
as soon as practicable of any action, suit, proceeding or investigation
involving him for which indemnity will or could be sought. With respect to any
action, suit, proceeding or investigation of which the Corporation is so
notified, the Corporation will be entitled to participate therein at its own
expense and/or to assume the defense thereof at its own expense, with legal
counsel reasonably acceptable to the Indemnitee. After notice from the
Corporation to the Indemnitee of its election so to assume such defense, the
Corporation shall not be liable to the Indemnitee for any legal or other
expenses subsequently incurred by the Indemnitee in connection with such claim,
other than as provided below in this Section 4. The Indemnitee shall have the
right to employ his own counsel in connection with such claim, but the fees and
expenses of such counsel incurred after notice from the Corporation of its
assumption of the defense thereof shall be at the expense of the Indemnitee
unless (i) the employment of counsel by the Indemnitee has been authorized by
the Corporation, (ii) counsel to the Indemnitee shall have reasonably concluded
that there may be a conflict of interest or position on any significant issue
between the Corporation and the Indemnitee in the conduct of the defense of such
action or (iii) the Corporation shall not in fact have employed counsel to
assume the defense of such action, in each of which cases the fees and expenses
of counsel for the Indemnitee shall be at the expense of the Corporation, except
as otherwise expressly provided by this Article. The Corporation shall not be
entitled, without the consent of the Indemnitee, to assume the defense of any
claim brought by or in the right of the Corporation or as to which counsel for
the Indemnitee shall have reasonably made the conclusion provided for in clause
(ii) above.
 
 
                                       -7-
 
<PAGE>   8
 
 
 
     5.   ADVANCE OF EXPENSES. Subject to the provisions of Section 6 below, in
the event that the Corporation does not assume the defense pursuant to Section 4
of this Article of any action, suit, proceeding or investigation of which the
Corporation receives notice under this Article, any expenses (including
attorneys' fees) incurred by an Indemnitee in defending a civil or criminal
action, suit, proceeding or investigation or any appeal therefrom shall be paid
by the Corporation in advance of the final disposition of such matter; PROVIDED,
HOWEVER, that the payment of such expenses incurred by an Indemnitee in advance
of the final disposition of such matter shall be made only upon receipt of an
undertaking by or on behalf of the Indemnitee to repay all amounts so advanced
in the event that it shall ultimately be determined that the Indemnitee is not
entitled to be indemnified by the Corporation as authorized in this Article.
Such undertaking shall be accepted without reference to the financial ability of
the Indemnitee to make such repayment.
 
     6.   PROCEDURE FOR INDEMNIFICATION. In order to obtain indemnification or
advancement of expenses pursuant to Section 1, 2, 3 or 5 of this Article, the
Indemnitee shall submit to the Corporation a written request, including in such
request such documentation and information as is reasonably available to the
Indemnitee and is reasonably necessary to determine whether and to what extent
the Indemnitee is entitled to indemnification or advancement of expenses. Any
such indemnification or advancement of expenses shall be made promptly, and in
any event within 60 days after receipt by the Corporation of the written request
of the Indemnitee, unless with respect to requests under Section 1, 2 or 5 the
Corporation determines, by clear and convincing evidence, within such 60-day
period that the Indemnitee did not meet the applicable standard of conduct set
forth in Section 1 or 2, as the case may be. Such determination shall be made in
each instance by (a) a majority vote of the directors of the Corporation
consisting of persons who are not at that time parties to the action, suit or
proceeding in question ("disinterested directors"), even though less than a
quorum, (b) a majority vote of a committee of disinterested directors designated
by a majority vote of disinterested directors, whether or not a quorum, (c) a
majority vote of a quorum of the outstanding shares of stock of all classes
entitled to vote for directors, voting as a single class, which quorum shall
consist of stockholders who are not at that time parties to the action, suit or
proceeding in question, (d) independent legal counsel (who may be regular legal
counsel to the Corporation), or (e) a court of competent jurisdiction.
 
     7.   REMEDIES. The right to indemnification or advances as granted by this
Article shall be enforceable by the Indemnitee in any court of competent
jurisdiction if the Corporation denies such request, in whole or in part, or if
no disposition thereof is made within the 60-day period referred to above in
Section 6. Unless otherwise provided by law, the burden of proving that the
Indemnitee is not entitled to
 
 
 
                                       -8-
 
<PAGE>   9
 
 
 
indemnification or advancement of expenses under this Article shall be on the
Corporation. Neither the failure of the Corporation to have made a determination
prior to the commencement of such action that indemnification is proper in the
circumstances because the Indemnitee has met the applicable standard of conduct,
nor an actual determination by the Corporation pursuant to Section 6 that the
Indemnitee has not met such applicable standard of conduct, shall be a defense
to the action or create a presumption that the Indemnitee has not met the
applicable standard of conduct. The Indemnitee's expenses (including attorneys'
fees) incurred in connection with successfully establishing his right to
indemnification, in whole or in part, in any such proceeding shall also be
indemnified by the Corporation.
 
     8.   SUBSEQUENT AMENDMENT. No amendment, termination or repeal of this
Article or of the relevant provisions of the General Corporation Law of Delaware
or any other applicable laws shall affect or diminish in any way the rights of
any Indemnitee to indemnification under the provisions hereof with respect to
any action, suit, proceeding or investigation arising out of or relating to any
actions, transactions or facts occurring prior to the final adoption of such
amendment, termination or repeal.
 
     9.   OTHER RIGHTS. The indemnification and advancement of expenses provided
by this Article shall not be deemed exclusive of any other rights to which an
Indemnitee seeking indemnification or advancement of expenses may be entitled
under any law (common or statutory), agreement or vote of stockholders or
disinterested directors or otherwise, both as to action in his official capacity
and as to action in any other capacity while holding office for the Corporation,
and shall continue as to an Indemnitee who has ceased to be a director or
officer, and shall inure to the benefit of the estate, heirs, executors and
administrators of the Indemnitee. Nothing contained in this Article shall be
deemed to prohibit, and the Corporation is specifically authorized to enter
into, agreements with officers and directors providing indemnification rights
and procedures different from those set forth in this Article. In addition, the
Corporation may, to the extent authorized from time to time by its Board of
Directors, grant indemnification rights to other employees or agents of the
Corporation or other persons serving the Corporation and such rights may be
equivalent to, or greater or less than, those set forth in this Article.
 
     10.  PARTIAL INDEMNIFICATION. If an Indemnitee is entitled under any
provision of this Article to indemnification by the Corporation for some or a
portion of the expenses (including attorneys' fees), judgments, fines or amounts
paid in settlement actually and reasonably incurred by him or on his behalf in
connection with any action, suit, proceeding or investigation and any appeal,
therefrom but not, however, for the total amount thereof, the Corporation shall
nevertheless indemnify the Indemnitee for
 
 
                                       -9-
 
<PAGE>   10
 
 
 
the portion of such expenses (including attorneys' fees), judgments, fines or
amounts paid in settlement to which the Indemnitee is entitled.
 
     11.  INSURANCE. The Corporation may purchase and maintain insurance, at its
expense, to protect itself and any director, officer, employee or agent of the
Corporation or another corporation, partnership, joint venture, trust or other
enterprise (including any employee benefit plan) against any expense, liability
or loss incurred by him in any such capacity, or arising out of his status as
such, whether or not the Corporation would have the power to indemnify such
person against such expense, liability or loss under the General Corporation law
of Delaware.
 
     12.  MERGER OR CONSOLIDATION. If the Corporation is merged into or
consolidated with another corporation and the Corporation is not the surviving
corporation, the surviving corporation shall assume the obligations of the
Corporation under this Article with respect to any action, suit, proceeding or
investigation arising out of or relating to any actions, transactions or facts
occurring prior to the date of such merger or consolidation.
 
     13.  SAVINGS CLAUSE. If this Article or any portion hereof shall be
invalidated on any ground by any court of competent jurisdiction, then the
Corporation shall nevertheless indemnify each Indemnitee as to any expenses
(including attorneys' fees) judgments, fines and amounts paid in settlement in
connection with any action, suit, proceeding or investigation, whether civil,
criminal or administrative, including an action by or in the right of the
Corporation, to the fullest extent permitted by any applicable portion of this
Article that shall not have been invalidated and to the fullest extent permitted
by applicable law.
 
     14.  DEFINITIONS. Terms used herein and defined in Section 145(h) and
Section 145(i) of the General Corporation Law of Delaware shall have the
respective meanings assigned to such terms in such Section 145(h) and Section
145(i).
 
     15.  SUBSEQUENT LEGISLATION. If the General Corporation Law of Delaware is
amended after adoption of this Article to expand further the indemnification
permitted to Indemnitees, then the Corporation shall indemnify such persons to
the fullest extent permitted by the General Corporation Law of Delaware, as so
amended.
 
     TENTH. The Corporation reserves the right to amend, alter, change or repeal
any provision contained in this Restated Certificate of Incorporation, in the
manner now or hereafter prescribed by statute and this Restated Certificate of
Incorporation, and all rights conferred upon stockholders herein are granted
subject to this reservation.
 
 
                                      -10-
 
<PAGE>   11
 
 
 
     ELEVENTH. This Article is inserted for the management of the business and
for the conduct of the affairs of the Corporation.
 
     1.   NUMBER OF DIRECTORS. The number of directors of the Corporation shall
not be less than three. The exact number of directors within the limitations
specified in the preceding sentence shall be fixed from time to time by, or in
the manner provided in, the Corporation's Bylaws.
 
     2.   CLASSES OF DIRECTORS. The Board of Directors shall be and is divided
into three classes: Class I, Class II and Class III. No director shall be
elected or appointed to a class if, as a result, one class shall have more than
one director more than any other class. If a fraction is contained in the
quotient arrived at by dividing the designated number of directors by three,
then, if such fraction is one-third, the extra director shall be a member of
Class I, and if such fraction is two-thirds, one of the extra directors shall be
a member of Class I and one of the extra directors shall be a member of Class
II, unless otherwise provided from time to time by resolution adopted by the
Board of Directors.
 
     3.   ELECTION OF DIRECTORS. Elections of directors need not be by written
ballot except as and to the extent provided in the Bylaws of the Corporation.
 
     4.   TERMS OF OFFICE. Each director (other than a director elected to fill
a vacancy in accordance with Section 8) shall serve for a term ending on the
date of the third annual meeting following the annual meeting at which such
director was elected; PROVIDED, that each initial director in Class I shall
serve for a term ending on the date of the annual meeting in 2000; each initial
director in Class II shall serve for a term ending on the date of the annual
meeting in 2001; and each initial director in Class III shall serve for a term
ending on the date of the annual meeting in 2002; and PROVIDED, FURTHER, that
the term of each director shall be subject to the election and qualification of
his successor and to his earlier death, resignation or removal.
 
     5.   ALLOCATION OF DIRECTORS AMONG CLASSES IN THE EVENT OF INCREASES OR
DECREASES IN THE NUMBER OF DIRECTORS. In the event of any increase or decrease
in the authorized number of directors, (i) each director then serving as such
shall nevertheless continue as a director of the class of which he is a member
and (ii) the newly created or eliminated directorships resulting from such
increase or decrease shall be apportioned by the Board of Directors among the
three classes of directors so as to ensure that no one class has more than one
director more than any other class. To the extent possible, consistent with the
foregoing rule, any newly created directorships shall be added to those classes
whose terms of office are to expire at the latest dates following such
allocation, and any newly eliminated directorships shall be subtracted from
those
 
 
                                      -11-
 
<PAGE>   12
 
 
 
classes whose terms of office are to expire at the earliest dates following such
allocation, unless otherwise provided from time to time by resolution adopted by
the Board of Directors.
 
     6.   QUORUM; ACTION AT MEETING. A majority of the directors at any time in
office shall constitute a quorum for the transaction of business. In the event
one or more of the directors shall be disqualified to vote at any meeting, then
the required quorum shall be reduced by one for each director so disqualified,
provided that in no case shall less than one-third of the number of directors
fixed pursuant to Section 1 above constitute a quorum. If at any meeting of the
Board of Directors there shall be less than such a quorum, a majority of those
present may adjourn the meeting from time to time. Every act or decision done or
made by a majority of the directors present at a meeting duly held at which a
quorum is present shall be regarded as the act of the Board of Directors unless
a greater number is required by law, by the Bylaws of the Corporation or by this
Restated Certificate of Incorporation.
 
     7.   REMOVAL. Directors of the Corporation may be removed only for cause by
the affirmative vote of the holders of at least two-thirds of the shares of
capital stock of the Corporation issued and outstanding and entitled to vote.
 
     8.   VACANCIES. Any vacancy in the Board of Directors, however occurring,
including a vacancy resulting from an enlargement of the board, shall be filled
only by a vote of a majority of the directors then in office, although less than
a quorum, or by a sole remaining director. A director elected to fill a vacancy
shall be elected to hold office until the next election of the class for which
such director shall have been chosen, subject to the election and qualification
of his successor and to his earlier death, resignation or removal.
 
     9.   STOCKHOLDER NOMINATIONS AND INTRODUCTION OF BUSINESS, ETC. Advance
notice of stockholder nominations for election of directors and other business
to be brought by stockholders before a meeting of stockholders shall be given in
the manner provided by the Bylaws of the Corporation.
 
     10.  AMENDMENTS TO ARTICLE. Notwithstanding any other provisions of law,
this Restated Certificate of Incorporation or the Bylaws of the Corporation,
each as amended, and notwithstanding the fact that a lesser percentage may be
specified by law, the affirmative vote of the holders of at least seventy-five
percent (75%) of the shares of capital stock of the Corporation issued and
outstanding and entitled to vote shall be required to amend or repeal, or to
adopt any provision inconsistent with, this Article ELEVENTH.
 
 
                                      -12-
 
<PAGE>   13
 
 
 
     TWELFTH. Stockholders of the Corporation may not take any action by written
consent in lieu of a meeting. Notwithstanding any other provisions of law, this
Restated Certificate of Incorporation or the Bylaws of the Corporation, each as
amended, and notwithstanding the fact that a lesser percentage may be specified
by law, the affirmative vote of the holders of at least seventy-five percent
(75%) of the shares of capital stock of the Corporation issued and outstanding
and entitled to vote shall be required to amend or repeal, or to adopt any
provision inconsistent with, this Article TWELFTH.
 
     THIRTEENTH. Special meetings of stockholders may be called at any time only
by the Chairman of the Board of Directors, the Chief Executive Officer (or if
there is no Chief Executive Officer, the President) or the Board of Directors.
Business transacted at any special meeting of stockholders shall be limited to
matters relating to the purpose or purposes stated in the notice of meeting.
Notwithstanding any other provision of law, this Restated Certificate of
Incorporation or the Bylaws of the Corporation, each as amended, and
notwithstanding the fact that a lesser percentage may be specified by law, the
affirmative vote of the holders of at least seventy-five percent (75%) of the
shares of capital stock of the Corporation issued and outstanding and entitled
to vote shall be required to amend or repeal, or to adopt any provision
inconsistent with, this Article THIRTEENTH.
 
 
 
                                      -13-
 
<PAGE>   14
 
 
 
         IN WITNESS WHEREOF, the Corporation has caused its corporate seal to be
affixed hereto and this Restated Certificate of Incorporation to be signed by
its President and Chief Executive Officer this ____ day of ___________, 1999.
 
                                      ASPECT MEDICAL SYSTEMS, INC.
 
 
                                      By: ______________________________________
                                          Nassib G. Chamoun
                                          President and Chief Executive Officer