<PAGE>

                        CERTIFICATE OF DESIGNATION

                                    of

                         SERIES B PREFERRED STOCK

                                    of

                             CONDUCTUS, INC.

                     (Pursuant to Section 151 of the
                    Delaware General Corporation Law)

          Conductus, Inc., a corporation organized and existing under the 
General Corporation Law of the State of Delaware (hereinafter called the 
"Corporation"), hereby certifies that the following resolution was adopted by 
the Board of Directors of the Corporation as required by Section 151 of the 
General Corporation Law at a meeting duly called and held on May 29, 1998:

          WHEREAS, the Amended and Restated Certificate of Incorporation of 
the Corporation authorizes the Preferred Stock (the "Preferred Stock") of the 
Corporation to be issued in series and authorizes its board of directors 
(the "Board") to determine the rights, preferences, privileges and 
restrictions granted to or imposed upon any wholly unissued series of 
Preferred Stock and to fix the number of shares and designation of any such 
series; and

          WHEREAS, the Board has designated an initial series of Preferred 
Stock designated as Series A Junior Participating Preferred Stock (the 
"Series A Preferred");

          RESOLVED, that a series of Preferred Stock shall be designated 
Series B Preferred Stock (the "Series B Preferred");

          RESOLVED FURTHER, that the number of shares constituting Series B 
Preferred shall be Four Million Five Hundred Thousand (4,500,000) shares; and

          RESOLVED FURTHER, that the Board hereby fixes and determines the 
rights, preferences, privileges and restrictions relating to the Series B 
Preferred as follows:

          1.   DIVIDEND RIGHTS OF SERIES B PREFERRED.  Subject to the rights 
of additional series of Preferred Stock that may be designated by the Board 
from time to time, including the rights of Series A Preferred, the holders of 
shares of Series B Preferred shall be entitled to receive dividends, at the 
rate of $0.162 per share of Series B Preferred (as such dollar amount shall 
be appropriately adjusted for stock dividends, stock combinations, 
recapitalization or the like, the "Quarterly Accrual Amount") on each March 
31, June 30, September 30 and December 31 (each, a "Quarterly Accrual Date") 
after the date on which such share of Series B Preferred 

<PAGE>

was issued (the "Original Issue Date" for such share), provided that the 
amount of dividends on the first Quarterly Accrual Date after the Original 
Issue Date shall equal the Quarterly Accrual Amount multiplied by a fraction 
(A) the numerator of which shall equal the number of days from and including 
the Original Issue Date for such share to and including such first Quarterly 
Accrual Date, and (B) the denominator of which is Ninety (90).  Such 
dividends shall be cumulative and shall accrue, whether or not earned or 
declared.  Any accumulation of dividends on the Series B Preferred shall not 
bear interest.  Cumulative dividends with respect to a share of Series B 
Preferred which are accrued, shall be paid (A) in shares of Common Stock of 
the Corporation ("Common Stock"), upon conversion of such share of Series B 
Preferred into Common Stock pursuant to Section 3 below, or (B) if such share 
of Series B Preferred is not so converted, upon the liquidation, dissolution 
or winding up of the Corporation as provided in Section 2(a).

     Any dividend or distribution which is declared by the Corporation  and 
payable with assets of the Corporation other than cash shall be governed by 
the provisions of Subsection 2(d) below.

     2.   LIQUIDATION PREFERENCE.

          (a)  Subject to the rights of additional series of Preferred Stock 
that may be designated by the Board from time to time, in the event of any 
liquidation, dissolution or winding up of the Corporation, either voluntarily 
or involuntarily, the holders of the Series B Preferred shall be entitled to 
receive, prior and in preference to any distribution of any of the assets of 
the Corporation to the holders of Common Stock, an amount per share equal to 
$2.70 (the "Original Series B Purchase Price") plus any accrued but unpaid 
dividends for each share of Series B Preferred then held by them, such 
amounts being adjusted to reflect stock dividends, stock splits, 
combinations, recapitalizations or the like after the Original Series B Issue 
Date. After payment to the holders of the Series B Preferred of the amounts 
set forth in this Section 2, the entire remaining assets and funds of the 
Corporation legally available for distribution, if any, shall be distributed 
among the holders of the Common Stock in proportion to the shares of Common 
Stock then held by them. If, upon the occurrence of such event, the assets 
thus distributed among the holders of the Series B Preferred shall be 
insufficient to permit the payment to such holders of the full aforesaid 
preferential amount, then the entire assets and funds of the Corporation 
legally available for distribution shall be distributed among the holders of 
the Series B Preferred in proportion to the number of shares of Series B 
Preferred then held by them.

          (b)  (i)    For purposes of this Section 2, a liquidation, 
dissolution or winding up of the Corporation shall, unless holders of a 
majority of the then outstanding shares of Series B Preferred elect 
otherwise, be deemed to be occasioned by, or to include, (A) the acquisition 
of the Corporation by another entity by means of any transaction or series of 
related transactions (including, without limitation, any reorganization, 
merger or consolidation but, excluding any merger effected exclusively for 
the purpose of changing the domicile of the Corporation) that results in the 
transfer of fifty percent (50%) or more of the outstanding voting power of 
the Corporation; or (B) a sale of all or substantially all of the assets of 
the Corporation.

                                       2
<PAGE>

               (ii)  In any of such event, if the consideration received by 
the Corporation is other than cash, its value will be deemed its fair market 
value. Any securities to be delivered to the holders of the Series B 
Preferred or Common Stock, as the case may be, shall be valued as follows:

                    (1)   If traded on a securities exchange or through  
          the Nasdaq National Market, the value shall be deemed to be the 
          average of the closing prices of the securities on such exchange 
          over the thirty-day period ending three (3) days prior to the 
          closing;

                    (2)  If actively traded over-the-counter, the value shall 
          be deemed to be the average of the closing bid or sale prices 
          (whichever is applicable) over the thirty-day period ending three 
          (3) days prior to the closing; and

                    (3)  If there is no active public market, the value shall 
          be the fair market value thereof, as mutually determined by the 
          Corporation and the holders of at least a majority of the then 
          outstanding shares of Series B Preferred.

               (iii)  In the event the requirements of this Subsection 2(b) 
are not complied with, the Corporation shall forthwith either:

                    (1)   cause such closing to be postponed until such time  
          as the requirements of this Section 2 have been complied with; or

                    (2)   cancel such transaction, in which event the 
          respective rights, preferences and privileges of the holders of the 
          Series B Preferred shall revert to and be the same as such rights, 
          preferences and privileges existing immediately prior to the date 
          of the first notice referred to in Subsection 2(b)(iv) below.

               (iv) The Corporation shall give each holder of record of 
Series B Preferred written notice of such impending transaction not later 
than twenty (20) days prior to the stockholders' meeting called to approve 
such transaction, or twenty (20) days prior to the closing of such 
transaction, whichever is earlier, and shall also notify such holders in 
writing of the final approval of such transaction.  The first of such notices 
shall describe the material terms and conditions of the impending transaction 
and the provisions of this Section 2, and the Corporation shall thereafter 
give such holders prompt notice of any material changes.  The transaction 
shall in no event take place sooner than twenty (20) days after the 
Corporation has given the first notice provided for herein or sooner than ten 
(10) days after the Corporation has given notice of any material changes 
provided for herein; provided, however, that such periods may be shortened 
upon the Corporation's receipt of written consent of the holders of at least 
a majority of the then outstanding shares of Series B Preferred entitled to 
such notice rights or similar notice rights.

                                       3
<PAGE>

     3.   CONVERSION.  The holders of the Series B Preferred shall have 
conversion rights as follows (the "Conversion Rights"):

          (a)  RIGHT TO CONVERT.   Each share of Series B Preferred shall be 
convertible, at the option of the holder thereof, at any time after the date 
six (6) months following the Original Issue Date of such share, at the office 
of the Corporation or any transfer agent for such stock, into such number of 
fully paid and nonassessable shares of Common Stock as is determined by 
dividing the Original Series B Purchase Price plus any accrued but unpaid 
dividends by the Conversion Price (as defined below) applicable to such 
share, determined as hereafter provided, in effect on the date the 
certificate is surrendered for conversion.  The initial "Conversion Price" 
per share for shares of Series B Preferred shall be the Original Series B 
Purchase Price; provided, however, that the Conversion Price for the Series B 
Preferred shall be subject to adjustment as set forth in subsection 3(d).

          (b)  AUTOMATIC CONVERSION.  Each share of Series B Preferred shall 
be automatically converted into shares of Common Stock at the Conversion 
Price in effect at the time upon the date specified by written consent or 
agreement of the holders of two-thirds of the then outstanding shares of 
Series B Preferred.

          (c)  MECHANICS OF CONVERSION.

               (i)    CONVERSION PURSUANT TO SECTION 3(a).  Before any holder 
of Series B Preferred shall be entitled to convert the same into shares of 
Common Stock, such holder shall surrender the certificate or certificates 
therefor, duly endorsed, at the office of the Corporation or of any transfer 
agent for the Series B Preferred, and shall give written notice to the 
Corporation at such office that he/she elects to convert the same, and shall 
state therein the name or names which he/she wishes the certificate or 
certificates for shares of Common Stock to be issued. The Corporation shall, 
as soon as practicable thereafter, issue and deliver at such office to each 
holder of Series B Preferred, or to his nominee or nominees, a certificate or 
certificates for the number of shares of Common Stock to which he/she shall 
be entitled. Such conversion shall be deemed to have been made immediately 
prior to the close of business on the date of such surrender of the shares of 
Series B Preferred to be converted, and the person or persons entitled to 
receive the shares of Common Stock issuable upon such conversion shall be 
treated for all purposes as the record holder or holders of such shares of 
Common Stock on such date.

               (ii)   CONVERSION PURSUANT TO SECTION 3(b).   If shares of 
Series B Preferred are automatically converted, written notice shall be 
delivered to the holder of such shares of Series B Preferred at the address 
last shown on the records of the Corporation for such holder or given by such 
holder to the Corporation for the purpose of notice or, if no such address 
appears or is given, at the place where the principal executive office of the 
Corporation is located, notifying such holder of the conversion to be 
effected, specifying the date on which such conversion is expected to occur, 
the number of shares of Series B Preferred to be converted and calling upon 
such holder to surrender to Corporation, in the manner and at the place 
designated, the certificate or certificates therefor.  Upon such conversion 
of the shares of Series B 

                                       4
<PAGE>

Preferred, holders shall surrender the certificate or certificates therefor, 
duly endorsed, at the office of the Corporation or of any transfer agent for 
the Series B Preferred, and shall state therein the name or names which 
he/she wishes the certificate or certificates for shares of Common Stock to 
be issued. The Corporation shall, as soon as practicable thereafter, issue 
and deliver at such office to each holder of Series B Preferred, or to his 
nominee or nominees, a certificate or certificates for the number of shares 
of Common Stock to which he/she shall be entitled. Any conversion of Series B 
Preferred pursuant to Section 3(b) shall be deemed to have been made 
immediately prior to the closing of the issuance and sale of shares as 
described in Section 3(b).

               (iii)  FRACTIONAL SHARES.  No fractional shares shall be 
issued upon conversion of the Series B Preferred.  In lieu of Corporation 
issuing any fractional shares to holders upon the conversion of the Series B 
Preferred, Corporation shall pay to such holders an amount equal to the 
product obtained by multiplying the Conversion Price by the fraction of a 
share not issued pursuant to the previous sentence.

          (d)  ADJUSTMENT OF CONVERSION RATE. The number of shares of Common 
Stock into which the Series B Preferred may be converted shall be subject to 
adjustment from time to time as follows:

          (i)    (A)  If the Corporation shall issue, after the date upon 
which any shares of Series B Preferred were first issued (the "Purchase 
Date") and prior to the date three years following the Purchase Date, any 
Additional Stock (as defined below) without consideration or for a 
consideration per share less than the Conversion Price for such series in 
effect immediately prior to the issuance of such Additional Stock, the 
Conversion Price for such series in effect immediately prior to each such 
issuance shall forthwith (except as otherwise provided in this clause (i)) be 
adjusted to a price equal to the price paid per share for such Additional 
Stock.

                 (B)  No adjustment of the Conversion Price for the Series B 
Preferred shall be made in an amount less than one cent per share, provided 
that any adjustments that are not required to be made by reason of this 
sentence shall be carried forward and shall be either taken into account in 
any subsequent adjustment made prior to three (3) years from the date of the 
event giving rise to the adjustment being carried forward, or shall be made 
at the end of three (3) years from the date of the event giving rise to the 
adjustment being carried forward.  Except to the limited extent provided for 
in subsections (E)(3) and (E)(4), no adjustment of such Conversion Price 
pursuant to this subsection 3(d)(i) shall have the effect of increasing the 
Conversion Price above the Conversion Price in effect immediately prior to 
such adjustment.

                 (C)  In the case of the issuance of Common Stock for cash, 
the consideration shall be deemed to be the amount of cash paid therefor 
before deducting any reasonable discounts, commissions or other expenses 
allowed, paid or incurred by the Corporation for any underwriting or 
otherwise in connection with the issuance and sale thereof.

                 (D)  In the case of the issuance of the Common Stock for a 
consideration in whole or in part other than cash, the consideration other 
than cash shall be 

                                       5
<PAGE>

deemed to be the fair value thereof as determined by the Board irrespective 
of any accounting treatment.

                 (E)  In the case of the issuance (whether before, on or 
after the applicable Purchase Date) of options to purchase or rights to 
subscribe for Common Stock, securities by their terms convertible into or 
exchangeable for Common Stock or options to purchase or rights to subscribe 
for such convertible or exchangeable securities, the following provisions 
shall apply for all purposes of this subsection 3(d)(i) and subsection 
3(d)(ii):

                 (1)  The aggregate maximum number of shares of Common Stock 
                      deliverable upon exercise (assuming the satisfaction of 
                      any conditions to exercisability, including without 
                      limitation, the passage of time, but without taking 
                      into account potential antidilution adjustments) of 
                      such options to purchase or rights to subscribe for 
                      Common Stock shall be deemed to have been issued at the 
                      time such options or rights were issued and for a 
                      consideration equal to the consideration (determined in 
                      the manner provided in subsections 3(d)(i)(C) and 
                      (d)(i)(D)), if any, received by the Corporation upon 
                      the issuance of such options or rights plus the minimum 
                      exercise price provided in such options or rights for 
                      the Common Stock covered thereby.

                 (2)  The aggregate maximum number of shares of Common Stock 
                      deliverable upon conversion of, or in exchange 
                      (assuming the satisfaction of any conditions to 
                      convertibility or exchangeability, including, without 
                      limitation, the passage of time, but without taking 
                      into account potential antidilution adjustments) for, 
                      any such convertible or exchangeable securities or upon 
                      the exercise of options to purchase or rights to 
                      subscribe for such convertible or exchangeable 
                      securities and subsequent conversion or exchange 
                      thereof shall be deemed to have been issued at the time 
                      such securities were issued or such options or rights 
                      were issued and for a consideration equal to the 
                      consideration, if any, received by the Corporation for 
                      any such securities and related options or rights 
                      (excluding any cash received on account of accrued 
                      interest or accrued dividends), plus the minimum 
                      additional consideration, if any, to be received by the 
                      Corporation upon the conversion or exchange of such 
                      securities or the exercise of any related options or 
                      rights (the consideration in each case to be determined 
                      in the manner provided in subsections 3(d)(i)(C) and 
                      (d)(i)(D)).

                 (3)  In the event of any change in the number of shares of 
                      Common Stock deliverable or in the consideration 
                      payable to the Corporation upon exercise of such 
                      options or rights or upon conversion of or in exchange 
                      for such convertible or exchangeable securities, 
                      including, but not 

                                       6
<PAGE>

                      limited to, a change resulting from the antidilution 
                      provisions thereof (unless such options or rights or 
                      convertible or exchangeable securities were merely 
                      deemed to be included in the numerator and denominator 
                      for purposes of determining the number of shares of 
                      Common Stock outstanding for purposes of subsection 
                      3(d)(i)(A)), the Conversion Price of the Series B 
                      Preferred, to the extent in any way affected by or 
                      computed using such options, rights or securities, 
                      shall be recomputed to reflect such change, but no 
                      further adjustment shall be made for the actual 
                      issuance of Common Stock or any payment of such 
                      consideration upon the exercise of any such options or 
                      rights or the conversion or exchange of such securities.

                 (4)  Upon the expiration of any such options or rights, the 
                      termination of any such rights to convert or exchange 
                      or the expiration of any options or rights related to 
                      such convertible or exchangeable securities, the 
                      Conversion Price of the Series B Preferred, to the 
                      extent in any way affected by or computed using such 
                      options, rights or securities or options or rights 
                      related to such securities (unless such options or 
                      rights were merely deemed to be included in the 
                      numerator and denominator for purposes of determining 
                      the number of shares of Common Stock outstanding for 
                      purposes of subsection 3(d)(i)(A)), shall be recomputed 
                      to reflect the issuance of only the number of shares of 
                      Common Stock (and convertible or exchangeable 
                      securities that remain in effect) actually issued upon 
                      the exercise of such options or rights, upon the 
                      conversion or exchange of such securities or upon the 
                      exercise of the options or rights related to such 
                      securities.

                 (5)  The number of shares of Common Stock deemed issued and 
                      the consideration deemed paid therefor pursuant to 
                      subsections 3(d)(i)(E)(1) and (2) shall be 
                      appropriately adjusted to reflect any change, 
                      termination or expiration of the type described in 
                      either subsection 3(d)(i)(E)(3) or (4).

          (ii)   "Additional Stock" shall mean any shares of Common Stock 
issued (or deemed to have been issued pursuant to subsection 3(d)(i)(E)) by 
the Corporation after the Purchase Date other than:

                 (A)  Common Stock issued pursuant to a transaction described 
in subsection 3(d)(iii) hereof;

                 (B)  Common Stock issued in a transaction or series of 
transactions resulting in gross proceeds to the Company of no more than 
$1,000,000;

                                       7
<PAGE>

                 (C)  Shares of Common Stock issuable or issued to employees, 
consultants, directors or vendors (if in transactions with primarily 
non-financing purposes) of the Corporation directly or pursuant to a stock 
option plan or restricted stock plan approved by the Board of the Corporation;

                 (D)  The issuance of securities pursuant to the conversion 
or exercise of convertible or exercisable securities, except as provided in 
Section 3(d)(i)(E); or

                 (E)   The issuance of securities in connection with a bona 
fide business acquisition of or by the Corporation, whether by merger, 
consolidation, sale of assets, sale or exchange of stock or otherwise.

          (iii)  ADJUSTMENTS FOR STOCK SPLITS AND SUBDIVISIONS.  In the event 
Corporation should at any time or from time to time after the date of 
issuance hereof fix a record date for the effectuation of a split or 
subdivision of the outstanding shares of Common Stock or the determination of 
holders of Common Stock entitled to receive a dividend or other distribution 
payable in additional shares of Common Stock or other securities or rights 
convertible into, or entitling the holder thereof to receive directly or 
indirectly, additional shares of Common Stock (hereinafter referred to as 
"Common Stock Equivalents") without payment of any consideration by such 
holder for the additional shares of Common Stock or the Common Stock 
Equivalents (including the additional shares of Common Stock issuable upon 
conversion or exercise thereof), then, as of such record date (or the date of 
such dividend distribution, split or subdivision if no record date is fixed), 
the Conversion Price shall be appropriately decreased so that the number of 
shares of Common Stock issuable upon conversion of the Series B Preferred 
shall be increased in proportion to such increase of outstanding shares.

          (iv)   ADJUSTMENTS FOR REVERSE STOCK SPLITS.  If the number of 
shares of Common Stock outstanding at any time after the date hereof is 
decreased by a combination of the outstanding shares of Common Stock, then, 
following the record date of such combination, the Conversion Price shall be 
appropriately increased so that the number of shares of Common Stock issuable 
on conversion hereof shall be decreased in proportion to such decrease in 
outstanding shares.

          (v)    RECAPITALIZATIONS.  If at any time or from time to time 
there shall be a recapitalization of the Common Stock (other than a 
subdivision, combination or merger or sale of assets transaction provided for 
elsewhere in this Section 3 or Section 2) provision shall be made so that the 
holders of the Series B Preferred shall thereafter be entitled to receive 
upon conversion of the Series B Preferred the number of shares of stock or 
other securities or property of the Corporation or otherwise, to which a 
holder of Common Stock deliverable upon conversion would have been entitled 
on such recapitalization. In any such case, appropriate adjustment shall be 
made in the application of the provisions of this Section 3 with respect to 
the rights of the holders of the Series B Preferred after the 
recapitalization to the end that the provisions of this Section 3 (including 
adjustment of the Conversion Price then in effect and the number of shares 
purchasable upon conversion of the Series B Preferred) shall be applicable 
after 

                                       8
<PAGE>

that event as nearly equivalent as may be practicable.

          (e)  NO IMPAIRMENT.  Except for taking the actions contemplated by 
Section 6 below upon obtaining the vote or consent set forth therein, the 
Corporation will not, by amendment of its Certificate of Incorporation or 
through any reorganization, transfer of assets, consolidation, merger, 
dissolution, issue or sale of securities or any other voluntary action, avoid 
or seek to avoid the observance or performance of any of the terms to be 
observed or performed hereunder by the Corporation, but it will at all times 
in good faith assist in the carrying out of all of the provisions of this 
Section 3 and in the taking of all such action as may be necessary or 
appropriate in order to protect the Conversion Rights of the holders of the 
Series B Preferred against impairment.

          (f)  CERTIFICATE AS TO ADJUSTMENTS.  Upon the occurrence of each 
adjustment or readjustment of the Conversion Price of the Series B Preferred 
pursuant to this Section 3, the Corporation, at its expense, shall promptly 
compute such adjustment or readjustment in accordance with the terms hereof 
and prepare and furnish to each holder of such Series B Preferred a 
certificate setting forth such adjustment or readjustment and showing in 
detail the facts upon which such adjustment or readjustment is based.  The 
Corporation shall, upon the written request at any time of any holder of 
Series B Preferred, furnish or cause to be furnished to such holder a like 
certificate setting forth (A) such adjustment and readjustment, (B) the 
Conversion Price at the time in effect, and (C) the number of shares of 
Common Stock and the amount, if any, of other property which at the time 
would be received upon the conversion of a share of Series B Preferred.


          (g)  NOTICES OF RECORD DATE.  In the event of any taking by the 
Corporation of the record of the holders of any class of securities for the 
purpose of determining the holders thereof who are entitled to receive any 
dividend (other than a cash dividend) or other distribution, the Corporation 
shall mail to each holder of Series B Preferred, at least twenty (20) days 
prior to the date specified herein, a notice specifying the date on which any 
such record is to be taken for the purpose of such dividend or distribution.

          (h)  RESERVATION OF STOCK.  The Corporation shall at all times 
reserve and keep available out of its authorized but unissued shares of 
Common Stock solely for the purpose of effecting the conversion of the shares 
of the Series B Preferred such number of its shares of Common Stock as shall 
from time to time be sufficient to effect the conversion of all outstanding 
shares of Series B Preferred; and if at any time the number of authorized but 
unissued shares of Common Stock shall not be sufficient to effect the 
conversion of all the then outstanding shares of the Series B Preferred, the 
Corporation will take such corporate action as may be necessary, in the 
opinion of its counsel, to increase its authorized but unissued shares of 
Common Stock to such number of shares as shall be sufficient for such purpose.

          (i)  NOTICES. Any notice required by the provisions of this Section 
3 to be given to the holders of shares of Series B Preferred shall be deemed 
given if deposited in the 

                                       9
<PAGE>

United States mail, postage prepaid, and addressed to each holder of record 
at his or her address appearing on the books of the Corporation.

     4.   REDEMPTION.  The Series B Preferred shall not be redeemable.

     5.   VOTING MATTERS.  Except as otherwise required by law, each share of 
Series B Preferred issued and outstanding shall have the number of votes 
equal to the number of shares of Common Stock into which the Series B 
Preferred is convertible pursuant to Section 3 hereof. The holder of each 
share of Series B Preferred shall be entitled to notice of any stockholders' 
meeting in accordance with the bylaws of the Corporation, and shall vote with 
the holders of the Common Stock upon any matter submitted to a vote of 
stockholders, except those matters required by law to be submitted to a class 
vote.

     6.   COVENANT.  In addition to any other rights provided by law, so long 
as any Series B Preferred shall be outstanding, the Corporation shall not, 
without first obtaining the affirmative vote or written consent of the 
holders of not less than seventy-five percent (75%), or two-thirds following 
the sale by the Company of shares of Series B Preferred having an aggregate 
purchase price of at least $6,000,000, of the then outstanding shares of all 
series of Preferred Stock voting together as a single class:

          (a)  alter or change the rights, preferences or privileges of the 
shares of the Series B Preferred;

          (b)  increase or decrease the authorized number of shares of the 
Series B Preferred; or

          (c)  authorize or create any new class of shares or additional 
series of Preferred Stock having rights, preferences or privileges prior to 
shares of the Series B Preferred,

          if such Series B Preferred would be adversely affected by such 
amendment in a manner different from other than outstanding shares of 
Preferred Stock (it being understood that, without limiting the foregoing, 
different shares of Preferred Stock shall not be affected differently because 
of differences in the amounts of their respective issue prices, liquidation 
preferences and redemption prices).

     7.   RESIDUAL RIGHTS.  All rights accruing to the outstanding shares of 
the Corporation not expressly provided for to the contrary herein shall be 
vested in the Common Stock.

                                       10
<PAGE>

          IN WITNESS WHEREOF, said Conductus, Inc. has caused this 
Certificate of Designation to be signed by the undersigned this 11th day of 
September, 1998.

                                       CONDUCTUS, INC.


                                             /s/  CHARLES E. SHALVOY
                                       ---------------------------------------
                                       Charles E. Shalvoy, President


Attest:



By:     /s/  BROOKS STOUGH
    -------------------------------
     Brooks Stough, Secretary