<PAGE>   1

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


                                    FORM 10-Q


                QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934


               For the Quarterly Period Ended  January 1, 1999
                                              ------------------

                      Commission file number  000-24923
                                             -------------


                             Conexant Systems, Inc.
             (Exact name of registrant as specified in its charter)


           Delaware                                      25-1799439
 (State or other jurisdiction                         (I.R.S. Employer
 incorporation or organization)                      Identification No.)


  4311 Jamboree Road, Newport Beach, California          92660-3095
    (Address of principal executive offices)              (Zip Code)


Registrant's telephone number including area code:   (949) 483-4600

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

                                Yes     No  X*
                                    ---    ---

--------------
*  Registrant's Registration Statement on Form 10 under the Securities Exchange
   Act of 1934 was declared effective on November 27, 1998. Prior thereto, 
   Registrant's business was reported as a business segment of Rockwell 
   International Corporation.

Number of shares of common stock outstanding as of January 31, 1999 is
94,881,504.



<PAGE>   2

                             CONEXANT SYSTEMS, INC.

                                      INDEX

<TABLE>
<CAPTION>

                                                                               Page No.
                                                                               --------
<S>             <C>                                                             <C>
PART I.   FINANCIAL INFORMATION:                                               

     Item 1.    Financial Statements:                                        

                Consolidated Condensed Balance Sheets--
                January 1, 1999 and September 30, 1998.........................   3

                Consolidated Condensed Statements of Operations--
                Three Months Ended January 1, 1999 and January 2, 1998.........   4

                Consolidated Condensed Statements of Cash Flows--
                Three Months Ended January 1, 1999 and January 2, 1998.........   5

                Notes to Consolidated Condensed Financial Statements...........   6

     Item 2.    Management's Discussion and Analysis of Financial
                Condition and Results of Operations ...........................  10

     Item 3.    Quantitative and Qualitative Disclosures About Market Risk.....  16


PART II.  OTHER INFORMATION:

     Item 1.    Legal Proceedings..............................................  17

     Item 4.    Submission of Matters to a Vote of Security Holders............  17

     Item 6.    Exhibits and Reports on Form 8-K...............................  17
</TABLE>


                                       2

<PAGE>   3
PART I. FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

                             CONEXANT SYSTEMS, INC.

                      CONSOLIDATED CONDENSED BALANCE SHEETS
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                         January 1,     September 30,
                                                                            1999            1998
                                                                         ----------     -------------
                                                                         (Unaudited)
<S>                                                                      <C>             <C>       
                                      ASSETS
CURRENT ASSETS:
Cash ..............................................................      $   13,282      $   14,000
Restricted cash ...................................................          64,000              --
Receivables (less allowance for doubtful accounts: January 1, 1999,
  $9,572; September 30, 1998, $8,975) .............................         135,780         166,386
Inventories, net (see Note 4) .....................................         142,050         200,926
Deferred income taxes .............................................          90,024         152,559
Assets held for disposal ..........................................              --          42,346
Other current assets ..............................................           9,517          10,735
                                                                         ----------      ----------

         Total current assets .....................................         454,653         586,952

PROPERTY, NET .....................................................         682,968         713,400
INTANGIBLE ASSETS, NET ............................................          50,489          52,552
OTHER ASSETS ......................................................          64,814          65,626
                                                                         ----------      ----------

         TOTAL ASSETS .............................................      $1,252,924      $1,418,530
                                                                         ==========      ==========

                       LIABILITIES AND SHAREHOLDERS' EQUITY

CURRENT LIABILITIES:
Short-term debt ...................................................      $   13,282      $   14,000
Accounts payable ..................................................          92,996         151,044
Accrued compensation and benefits .................................          32,839          37,111
Accrued litigation - Celeritas (see Note 5) .......................          65,000          65,000
Other current liabilities .........................................          85,768          63,108
                                                                         ----------      ----------

         Total current liabilities ................................         289,885         330,263

OTHER LIABILITIES AND CONTINGENCIES ...............................          65,967          78,892

SHAREHOLDERS' EQUITY:
Rockwell's net investment (September 30, 1998) ....................              --       1,009,375
Preferred stock (25,000 shares authorized, no shares issued
  or outstanding) .................................................              --              --
Common stock (500,000 shares authorized, 94,882 issued and 
  outstanding) ....................................................          94,882              --
Additional paid-in capital ........................................         802,190              --
                                                                         ----------      ----------
         Total shareholder's equity ...............................         897,072       1,009,375
                                                                         ----------      ----------

         TOTAL LIABILITY AND SHAREHOLDERS' EQUITY .................      $1,252,924      $1,418,530
                                                                         ==========      ==========
</TABLE>


            See notes to consolidated condensed financial statements.


                                       3
<PAGE>   4

                             CONEXANT SYSTEMS, INC.

                 CONSOLIDATED CONDENSED STATEMENTS OF OPERATIONS
                                   (UNAUDITED)
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                Three Months Ended
                                                             -------------------------
                                                             January 1,      January 2,
                                                                1999            1998
                                                             ---------       ---------
<S>                                                          <C>             <C>      
Net sales .............................................      $ 294,678       $ 383,452
Cost of sales .........................................        221,680         208,509
                                                             ---------       ---------

GROSS MARGIN ..........................................         72,998         174,943

Research and development ..............................         69,553          82,093
Selling, general and administrative ...................         64,016          59,542
Special charges - Rockwell Retained Assets (see Note 2)         20,000              --
Special charges - Other (see Note 3) ..................         17,906              --
                                                             ---------       ---------

OPERATING (LOSS) EARNINGS .............................        (98,477)         33,308
Other income, net .....................................          1,163           4,483
                                                             ---------       ---------


(LOSS) INCOME BEFORE INCOME TAXES .....................        (97,314)         37,791
(Benefit) provision for income taxes ..................        (40,191)         17,225
                                                             ---------       ---------

NET (LOSS) INCOME .....................................      $ (57,123)      $  20,566
                                                             =========       =========
</TABLE>

            See notes to consolidated condensed financial statements.


                                       4
<PAGE>   5

                             CONEXANT SYSTEMS, INC.

                 CONSOLIDATED CONDENSED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                     Three Months Ended
                                                                  -------------------------
                                                                  January 1,     January 2,
                                                                     1999           1998
                                                                  ----------     ----------
<S>                                                                <C>            <C>     
OPERATING ACTIVITIES:
Net (loss) income ...........................................      $(57,123)      $ 20,566
Adjustments to net (loss) income to arrive at cash
   provided by (used in) operating activities:
     Depreciation and amortization ..........................        51,764         47,170
     Deferred income taxes ..................................        11,564         (6,736)
     Special charges - Rockwell Retained Assets (see Note 2)         20,000             --
     Special charges - Other (see Note 3) ...................        17,906             --

     Changes in assets and liabilities:
         Receivables ........................................        30,606         11,792
         Inventories ........................................        58,876        (30,839)
         Accounts payable ...................................       (58,048)       (28,905)
         Other current liabilities ..........................        16,771         29,555
         Other ..............................................       (35,310)       (43,003)
                                                                   --------       --------

              CASH PROVIDED BY (USED IN) OPERATING ACTIVITIES        57,006           (400)
                                                                   --------       --------

INVESTING ACTIVITIES:
Capital expenditures ........................................       (14,845)       (42,684)
                                                                   --------       --------

              CASH USED IN INVESTING ACTIVITIES .............       (14,845)       (42,684)
                                                                   --------       --------

FINANCING ACTIVITIES:
Decrease in short-term borrowings ...........................          (718)            --
Payments of long-term debt ..................................            (7)           (33)
Net transfers from Rockwell .................................        21,846         43,117
Restricted cash transferred by Rockwell .....................       (64,000)            --
                                                                   --------       --------

              CASH (USED IN) PROVIDED BY FINANCING ACTIVITIES       (42,879)        43,084
                                                                   --------       --------

DECREASE IN CASH ............................................          (718)            --
CASH AT BEGINNING OF PERIOD .................................        14,000         14,000
                                                                   --------       --------

CASH AT END OF PERIOD .......................................      $ 13,282       $ 14,000
                                                                   ========       ========
</TABLE>


Non-cash activity: During the three months ended January 1, 1999, the Company
transferred its wafer fabrication facilities in Colorado Springs, Colorado (and
the related tax benefit) with a book value of $58 million to Rockwell as well as
certain other tax benefits of $23 million related to the Celeritas litigation.

            See notes to consolidated condensed financial statements.


                                       5
<PAGE>   6

                             CONEXANT SYSTEMS, INC.

              NOTES TO CONSOLIDATED CONDENSED FINANCIAL STATEMENTS


1.  BASIS OF PRESENTATION

On December 31, 1998, Conexant Systems, Inc. (formerly named Rockwell
Semiconductor Systems, Inc.) (the Company or Conexant), became an independent,
separately traded, publicly-held company when Rockwell International Corporation
(Rockwell) spun off its semiconductor systems business (Semiconductor Systems)
by means of the distribution (the Distribution) of all the outstanding shares of
common stock of the Company to the shareholders of Rockwell in a tax-free
spin-off. In the Distribution, each Rockwell shareholder received one share of
the Company's common stock (including an associated preferred share purchase
right) for every two shares of Rockwell common stock owned on December 11, 1998.

The consolidated condensed financial statements of Conexant have been prepared
in accordance with generally accepted accounting principles, which require
management to make estimates and assumptions that affect the amounts reported in
the financial statements. Actual results could differ from those estimates. In
the opinion of the management of Conexant, the unaudited financial statements
contain all adjustments, consisting of adjustments of a normal recurring nature,
as well as the special charges recorded in the first quarter of 1999 (see Note 2
and 3), necessary to present fairly the financial position, results of
operations, and cash flows for the periods presented. These statements should be
read in conjunction with the Company's Registration Statement on Form 10. The
results of operations for the three-month period ended January 1, 1999 are not
necessarily indicative of the results that may be expected for the full year.

The accompanying consolidated condensed financial statements present the
historical financial position, results of operations, and cash flows of
Semiconductor Systems, as it was spun off, and exclude the assets, liabilities,
and results of operations of non-semiconductor businesses retained by Rockwell.
These financial statements are not necessarily indicative of what the financial
position, results of operations, or cash flows would have been had Conexant been
an independent public company during the periods presented.

Rockwell provides certain services to the Company, including payroll and
employee benefits administration, data processing and telecommunications
services, and research and development activities. Rockwell also administers
certain programs in which the U.S. operations of Conexant participate, including
active medical and insurance programs. Costs for these services and programs are
billed to Conexant based on actual usage and are included in Conexant's
Consolidated Condensed Statements of Operations. Management believes that the
methods of billing these costs are reasonable and that the costs charged to
Conexant are approximately those which would have been incurred on a stand-alone
basis. As of January 1, 1999, the nature and term of services provided to
Conexant by Rockwell, including such services as payroll and employee benefits
administration, data processing, and research and development, became subject to
a transition agreement. The cost of the services to be billed by Rockwell is
approximately equal to the amounts previously billed and included in the 
historical financial statements.


                                       6
<PAGE>   7

Rockwell has historically provided management services to Conexant, including
such services as corporate oversight, financial, legal, tax, corporate
communications, and human resources. The costs of providing these services have
been allocated to Conexant based on sales in proportion to total Rockwell sales
and are included in selling, general and administrative expense in the
Consolidated Condensed Statements of Operations. Management believes that the
method of allocating these costs to Conexant is reasonable and the amount is
approximately equal to the cost of providing these services on a stand-alone
basis. These services were substantially discontinued after the Distribution.

Prior to January 1, 1999, Conexant's U.S., and certain of its non-U.S.,
operations participated in Rockwell's centralized cash management systems which
managed all of the Company's cash activities, including cash receipts and
disbursements. Accordingly, the consolidated condensed financial statements
exclude debt and interest income and expense in countries with centralized cash
management systems. Accounts payable includes $16 million as of January 1, 1999
and $8 million as of January 2, 1998 related to outstanding checks drawn on U.S.
centralized disbursement accounts. Conexant has no other financing or debt
arrangements with Rockwell. As of January 1, 1999, such cash management services
by Rockwell were discontinued.

In connection with the Distribution, Rockwell transferred cash balances of
approximately $13 million and an equal amount of short-term debt to Conexant.

Prior to the Distribution, the Company distributed its wafer fabrication
facilities in Colorado Springs, Colorado (and the related tax benefit) to
Rockwell. The transition agreement with Rockwell provides for continued
occupancy of the Colorado Springs facilities by Conexant through April 30, 1999
pursuant to a triple-net lease under which Conexant will pay all costs of the
facilities.

2.  SPECIAL CHARGES - ROCKWELL RETAINED ASSETS

In the first fiscal quarter of 1999, Conexant recorded a special charge for an
additional asset impairment of $20 million for the Colorado Springs wafer
fabrication facilities as a result of Rockwell's decision to further write-down
the facilities, which were retained by Rockwell as part of the spin-off. This
non-cash charge is required to be reported in the Company's last quarter as a
subsidiary of Rockwell.

3.  SPECIAL CHARGES - OTHER

In the fourth fiscal quarter of 1998, Conexant restructured its business and
recorded special charges of $147 million. In the first fiscal quarter of 1999,
Conexant recorded additional special charges of $18 million. The additional
charges include approximately $17 million relating to the Voluntary Early
Retirement Program (VERP) and $1 million relating to equipment decommission and
contract cancellations at the Colorado Springs wafer fabrication facilities. At
January 1, 1999, $37.7 million of the accruals for the special charges remained
on the Company's balance sheet. The restructuring actions are expected to be
substantially completed by the end of fiscal year 1999.


                                       7
<PAGE>   8

4.  INVENTORIES

Inventories are summarized as follows (in thousands):

<TABLE>
<CAPTION>
                                                 January 1,   September 30,
                                                    1999          1998
                                                 ----------   -------------
<S>                                               <C>           <C>     
     Finished goods, net ...................      $ 47,300      $ 71,328
     Work-in-process, net ..................        78,444       107,002
     Raw materials, parts, and supplies, net        16,306        22,596
                                                  --------      --------
     Inventories, net ......................      $142,050      $200,926
                                                  ========      ========
</TABLE>


5.  CONTINGENT LIABILITIES

Claims have been asserted against Conexant for utilizing the intellectual
property rights of others in certain of the Company's products. The resolution
of these matters may result in the negotiation of a license agreement, a
settlement, or the resolution of such claims through arbitration or litigation.

In September 1995, Celeritas Technologies, Ltd. filed suit against Rockwell for
patent infringement, misappropriation of trade secrets, and breach of contract
relating to cellular telephone data transmission technology utilized in certain
modem products produced by the Company. In July 1997, the court entered a
judgment awarding damages of $57 million, plus interest. On July 20, 1998, the
U.S. Court of Appeals for the Federal Circuit affirmed the trial court's
judgment based on breach of contract. As of September 30, 1998, $65 million was
reserved for this matter. On January 19, 1999, the U.S. Supreme Court denied
Rockwell's petition for certiorari. During the first fiscal quarter of 1999,
Rockwell contributed $64 million into an escrow account that will be used to
satisfy the Company's obligation with respect to this matter.

Various other lawsuits, claims, and proceedings have been or may be instituted
or asserted against the Company relating to the conduct of its business,
including those pertaining to product liability, safety and health,
environmental, and employment matters. Although the outcome of litigation cannot
be predicted with certainty and some lawsuits, claims, or proceedings may be
disposed of unfavorably to Conexant, management believes the disposition of
matters which are pending or asserted will not have a material adverse effect on
the Company's financial statements.

Conexant has assumed all contingent liabilities (including those in respect of
intellectual property and environmental matters) related to current and former
operations of Semiconductor Systems.


                                       8
<PAGE>   9

6.  FINANCING AGREEMENT

On December 21, 1998, Conexant entered into a three-year $350 million secured
revolving loan facility (the Credit Facility) with a group of banks. Loans under
the Credit Facility are to be used for working capital needs and other general
corporate purposes. The Credit Facility is guaranteed by substantially all of
the Company's domestic subsidiaries. It is also secured by (i) a first-priority
security interest in substantially all domestic assets of the Company and its
domestic subsidiaries and (ii) a pledge of the stock of the Company's domestic
and foreign subsidiaries, subject to certain exceptions.

Loans obtained under the Credit Facility will bear interest at a rate per annum
equal, at the election of the Company, to either (i) a base rate (ABR), which is
the higher of Credit Suisse First Boston's prime rate and 0.50 percent over the
federal funds rate or (ii) the London interbank offered rate for offshore dollar
deposits (LIBOR); plus, in either case, a variable margin. For the first six
months following the Distribution, the margin will be fixed at 75 basis points
for ABR-based loans and 175 basis points for LIBOR-based loans. After that, the
margin will be based on the Company's total debt to capitalization ratio. The
Company will pay a facility fee on the unused amount of the Credit Facility at a
per annum rate that will vary depending on the same criteria used to determine
the interest rate margin. The Company also will pay other customary fees.

The Credit Facility also contains, among other terms, representations and
warranties, conditions precedent, covenants, mandatory and voluntary prepayment
provisions and events of default customary for facilities of this type.
Borrowings under the Credit Facility are limited to $250 million prior to
receipt of Conexant's 1999 second fiscal quarter financial results. No
amounts were outstanding under the facility at January 1, 1999. On January 4,
1999, the Company borrowed $100 million under the Credit Facility.

7.  PRO-FORMA (LOSS) EARNINGS PER SHARE

For all periods presented, the number of pro-forma weighted average shares
outstanding and common share equivalents used in the (loss) earnings per share
calculation set forth below was based upon the weighted average number of
Rockwell shares outstanding and Rockwell common share equivalents for the
applicable period, adjusted for the distribution ratio in the Distribution of
one share of the Company's common stock for every two shares of Rockwell common
stock.

In connection with the Distribution, outstanding options to purchase Rockwell
common stock held by Conexant employees were converted into options to purchase
shares of Conexant common stock based on a formula designed to preserve the
intrinsic value of the options. Also, outstanding options to purchase Rockwell
common stock held by certain other optionholders who were not Conexant employees
were replaced with options to purchase shares of Rockwell common stock and
Conexant common stock, based on a formula also designed to preserve the
intrinsic value of the options. Pursuant to these adjustments, the Company
issued options for approximately 10,100,000 shares of Conexant common stock.

The options to purchase shares of the Company's common stock that were
outstanding at January 1, 1999 were not included in the computation of diluted
loss per share for the three months ended January 1, 1999, as their effect was
antidilutive.


                                       9
<PAGE>   10

Pro-forma basic and diluted (loss) earnings per share (in thousands, except per
share amounts):

<TABLE>
<CAPTION>
                                                  January 1,     January 2,
                                                     1999           1998
                                                  ----------     ----------
<S>                                                <C>            <C>     
     Net (loss) income ......................      $(57,123)      $ 20,566
     Pro-forma weighted average common shares        95,935        108,200
     Pro-forma (loss) earnings per share ....      $  (0.60)      $   0.19
</TABLE>

8.  SUBSEQUENT EVENTS

On January 4, 1999, the Company granted options to purchase approximately
7,738,000 shares of Conexant common stock and approximately 1,027,000 shares of
Conexant restricted stock under the Company's 1999 Long-Term Incentives Plan and
Directors Stock Plan. The per share exercise price for the options is $18.8125,
the closing price per share of Conexant common stock reported on the Nasdaq
National Market System on the date of grant. The options become exercisable
annually in approximately 25 percent increments beginning with the first
anniversary of the grant date.

The restricted stock grants consist of time vesting and performance accelerated
grants. The time vesting restricted stock generally will be restricted for a two
year period and will fully vest on the second anniversary of the grant date. For
the performance accelerated stock, 50 percent will vest upon the completion of
twenty consecutive trading days during which the fair market value of the stock
on each such trading day is at least 50 percent higher than the value of the
stock on the grant date and the remaining 50 percent will vest upon the
completion of twenty consecutive trading days during which the fair market value
of the stock on each such trading day is at least 100 percent higher than the
value of the stock on the grant date, provided that no performance accelerated
stock will vest prior to one year after the date of grant. In any event, the
performance accelerated stock will fully vest on the eighth anniversary of the
grant date.

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS.

This information should be read in conjunction with the unaudited consolidated
condensed financial statements and the notes thereto included in Item 1 of this
Quarterly Report and the audited combined financial statements and notes thereto
and Management's Discussion and Analysis of Financial Condition and Results of
Operations contained in the Company's Registration Statement on Form 10.

The results of operations set forth in this Quarterly Report reflect the
Company's operations as a subsidiary of Rockwell. The results of operations may
not be indicative of the results of operations of the Company as a stand-alone
entity for the respective time periods shown herein.


                                       10
<PAGE>   11

RESULTS OF OPERATIONS - FIRST QUARTER OF 1999 COMPARED TO FIRST QUARTER OF 1998

The following table summarizes the Company's operating results for the first
fiscal quarter ended January 1, 1999 (Q1 1999), as compared to the first fiscal
quarter ended January 2, 1998 (Q1 1998) (dollars are in thousands and
percentages are expressed as a percentage of net sales):

<TABLE>
<CAPTION>
                                                       Three Months Ended
                                        ------------------------------------------------
                                                01/01/99                  01/02/98
                                        ----------------------     ---------------------
<S>                                     <C>             <C>        <C>            <C>   
     Net sales ...................      $ 294,678       100.0%     $ 383,452      100.0%
     Cost of sales ...............        221,680        75.2        208,509       54.4
                                        ---------       -----      ---------      -----
     Gross margin ................         72,998        24.8        174,943       45.6

     Research and development ....         69,553        23.6         82,093       21.4
     Selling, general and
          administrative .........         64,016        21.7         59,542       15.5
     Special charges - Rockwell
          Retained Assets ........         20,000         6.8             --         --
     Special charges - Other .....         17,906         6.1             --         --
                                        ---------       -----      ---------      -----
     Operating (Loss) earnings ...        (98,477)      (33.4)        33,308        8.7
     Other income, net ...........          1,163         0.4          4,483        1.2
                                        ---------       -----      ---------      -----
     (Loss) income before taxes ..        (97,314)      (33.0)        37,791        9.9
     (Benefit) provision for taxes        (40,191)      (13.6)        17,225        4.5
                                        ---------       -----      ---------      -----
     Net (loss) income ...........      $ (57,123)      (19.4)%    $  20,566        5.4%
                                        =========       =====      =========      =====
</TABLE>


                                       11
<PAGE>   12
Revenues of $294.7 million in Q1 1999 were $88.8 million, or 23 percent, lower
than in Q1 1998. This decrease was due primarily to a 39 percent reduction in
prices on analog PC modem products, despite the unit shipments increasing
slightly. In the Company's Personal Imaging platform, a 41 percent reduction in
facsimile modem unit shipments and 14 percent price declines, resulting
principally from the continuing effects of the Asia-Pacific economic recession,
also contributed to the reduction. These decreases and a slight decrease in
Digital Infotainment revenue offset a 13 percent revenue gain recorded in two of
the Company's other platforms (Network Access and Wireless Communications).

The following table summarizes the Company's revenues by platform for Q1 1999 as
compared to Q1 1998 (dollars are in thousands and percentages are expressed as a
percentage of total net sales):

<TABLE>
<CAPTION>
                                                Three Months Ended
                                  ------------------------------------------------
                                           01/01/99                 01/02/98
                                  ----------------------    ----------------------
<S>                               <C>              <C>      <C>              <C>  
     Personal Computing ....      $152,277         51.7%    $232,696         60.6%
     Personal Imaging ......        16,016          5.4       32,481          8.5
     Network Access ........        41,727         14.2       34,027          8.9
     Digital Infotainment ..        39,444         13.4       41,101         10.7
     Wireless Communications        45,214         15.3       43,147         11.3
                                  --------        -----     --------        ----- 
     Total .................      $294,678        100.0%    $383,452        100.0%
                                  ========        =====     ========        =====
</TABLE>

Cost of sales of $221.7 million in Q1 1999 increased by $13.2 million, or 
6 percent, compared to Q1 1998. The increase was driven principally by
approximately $40 million of unusually high inventory costs as a result of lower
manufacturing capacity utilization over the last four months of fiscal 1998.
Gross margins decreased from 46 percent of sales in Q1 1998 to 25 percent in Q1
1999 primarily due to the reduction in analog PC modem prices coupled with the
unusually high inventory costs.

Research and development (R&D) expenses in Q1 1999 of $69.6 million were $12.5
million, or 15 percent, lower than in Q1 1998. The decrease was driven
principally by certain cost reduction actions taken in the fourth quarter of
1998 (Q4 1998) to reduce the Company's overall cost structure. These actions
included headcount reductions, design center closures, and project
cancellations.

Selling, general and administrative (SG&A) expenses in Q1 1999 of $64.0 million
were $4.5 million, or 8 percent, higher than in Q1 1998. The increase was due in
part to $13 million of unusual costs relating to the Company's corporate
identity campaign, payroll-related restructuring costs, and corporate set-up
expenses. These cost increases were partially offset by the cost reduction
actions undertaken in Q4 1998.

In September 1998, the Company recorded special charges of approximately $103
million related to its decision to close and dispose of its wafer fabrication
facilities in Colorado Springs, Colorado. Prior to the Distribution, the Company
distributed the facilities (and the related tax benefit) to Rockwell. Following
the Distribution, Rockwell decided to further writedown the value of the
facilities. The accounting rules governing the spin-off of the Company require
that 


                                       12
<PAGE>   13

Conexant report this additional $20.0 million non-cash charge in its last
quarter as a subsidiary of Rockwell.

The Company recorded other charges in the first quarter of $17.9 million,
consisting principally of $16.7 million for the Voluntary Early Retirement
Program offered by the Company in September 1998, and completed during the first
quarter of 1999.

Other income, net, decreased year over year by $3.3 million as a result of a
cash payment that was received in Q1 1998 in connection with a contract
cancellation.

The income tax benefit in the quarter was $40.2 million, as a result of the loss
for the quarter. The effective tax rate for Q1 1999 is 41.3 percent. The
effective tax rate includes state and local tax credits and federal research and
development credits.

RECENT DEVELOPMENTS

On January 19, 1999, the United States Supreme Court denied the Company's
petition for certiorari on the Celeritas intellectual property matter.
Consequently, the Company will be required to pay $57.6 million plus interest
and costs. Rockwell has provided $64.0 million in cash to fund this obligation
in an escrow account shown as restricted cash on the balance sheet. All income
statement charges associated with this matter were recorded in earlier quarters.

LIQUIDITY AND CAPITAL RESOURCES

Cash provided by operating activities was $57.0 million for Q1 1999 compared to
$0.4 million of cash used by operating activities in Q1 1998. Net operating cash
flows increased over the same period due primarily to a net decrease in
inventories of $58.9 million, reflecting the results of the Company's initial
efforts to reduce inventories in addition to adjustments required to revalue
inventories to fiscal 1999 actual costs made in Q1 1999. In addition, net
receivables were reduced by $30.6 million, driven by an improved rate of
collections relating to the timing of the sales throughout the quarter coupled
with additional reserves for anticipated price adjustments. The improvement in
net operating cash flow was also impacted by the adjustments to the net loss as
a result of the non-cash special charges of $37.9 million. These items were
partially offset by a $58.0 million decrease in trade payables compared with a
$28.9 million decrease in trade payables in Q1 1998.

Investing activities used $14.8 million in cash during Q1 1999 compared to $42.7
million in Q1 1998, all of which related to capital expenditures that were at
unusually low levels in Q1 1999 due to the timing of investments in additional
capacity and new process technologies.

The Company's financing activities used cash of $42.9 million during Q1 1999
compared to $43.1 million of cash provided by financing activities during Q1
1998. Financing sources of cash for both of these periods were predominantly
transfers of cash from Rockwell.

In December 1998, the Company and three of its subsidiaries entered into a
three-year $350 million senior secured revolving loan facility (the Credit
Facility) with a group of banks. The Credit Facility includes facilities for
revolving loans and swingline loans in multiple currencies and letters of 


                                       13
<PAGE>   14

credit. The Credit Facility is guaranteed by substantially all of the Company's
domestic subsidiaries. It is also secured by (i) a first-priority security
interest in substantially all domestic assets of the Company and its domestic
subsidiaries and (ii) a pledge of the stock of the Company's domestic and
foreign subsidiaries, subject to certain exceptions. For further details on
the credit facility see Note 6.

The Credit Facility contains, among other terms, representations and warranties,
conditions precedent, covenants, mandatory and voluntary prepayment provisions
and events of default customary for facilities of this type. Covenants include
certain restrictions on capital expenditures, consolidations and mergers, sales
of assets, incurrence of indebtedness and creation of liens and encumbrances.
The Credit Facility includes various financial covenants, including a minimum
net worth requirement and required financial ratios in respect of (i) earnings
before interest, taxes, depreciation and amortization (EBITDA) to interest
expense, (ii) debt to EBITDA and (iii) cash, cash equivalents and net accounts
receivable classified as current assets to current liabilities.

On January 4, 1999, the Company borrowed $100 million under the Credit Facility.

The Company believes that its existing sources of liquidity and cash expected to
be generated from future operations are sufficient to fund operations, capital
expenditures, and research and development efforts for the foreseeable future.

OUTLOOK

Based on the Company's first quarter performance and current order visibility,
the expectations of the Company for the second quarter are stronger than they
were at the beginning of fiscal 1999. The revenue decline anticipated in the
Company's seasonally weak second quarter should be between five and ten percent,
less than previously expected. In addition, with improved factory utilization
and elimination of costs associated with the Company's restructuring and
spin-off programs, the Company believes gross margins will be between 38 and 42
percent of revenues. The Company also expects operating expenses to decline by
approximately 10 percent 


                                       14
<PAGE>   15

from the reported first quarter levels. The Company believes that it is on track
for a return to profitability in the second half of calendar 1999.

YEAR 2000 READINESS DISCLOSURE

Conexant is addressing the impact of the Year 2000 on each of five major areas:
the Company's products, business systems (computer systems that handle business
processes), infrastructure (servers, desktop computers, networks, telecom
systems and software), manufacturing systems (computer systems used in the
manufacturing process) and suppliers (critical materials suppliers to the
business). Each of the five areas is undergoing the following process to ensure
readiness for the Year 2000. First, in the inventory phase, all Conexant assets
are inventoried to identify those that have any type of software or hardware
with Year 2000-related issues. Second, in the assessment phase, all inventoried
items are assessed to confirm that a Year 2000-related issue is present and the
extent of remediation required. Third, in the strategy phase, a remediation
strategy is created to ensure that all critical systems are upgraded to be Year
2000 ready by December 31, 1999. Fourth, in the conversion/upgrade phase,
upgrades are performed on all items identified in the assessment and strategy
phases. Finally, in the certification phase, all upgraded items receive final
certification testing to verify Year 2000 readiness. Conexant has completed the
inventory phase for all five areas. In addition, it has completed the assessment
and strategy phases and is currently in the conversion and certification phases
for the products, business systems, infrastructure, and manufacturing systems
areas. The Company is currently in the assessment and strategy phase for the
supplier area. Conexant is integrating its testing efforts with SEMATECH, a
consortium of semiconductor manufacturing companies, to ensure best practice
testing. The manufacturing systems, hardware systems, and software applications
areas are being tested under the SEMATECH guidelines.

The Company's greatest area of uncertainty centers primarily in the supplier and
manufacturing areas, due to the number of equipment and materials suppliers
involved and their various stages of readiness for Year 2000. In particular, the
Company is dependent on semiconductor equipment manufacturers to supply the
upgrades required to remediate Year 2000 issues in the manufacturing systems
area and suppliers to upgrade their systems to ensure an uninterrupted supply of
materials. A Year 2000-related failure by a significant equipment or materials
supplier could result in the temporary slowdown of production by the Company,
the duration of which the Company reasonably estimates would be not more than a
few days. As a result, the Company's contingency planning centers heavily on the
supplier and manufacturing systems areas. For the top five to ten percent of its
critical materials and manufacturing suppliers, the Company is performing
on-site audits and intends to monitor specific Year 2000-based milestones to
ensure readiness. In the event a supplier does not meet the Company's milestones
for Year 2000 readiness, the Company is identifying specific target dates
(beginning as early as April 1999) for 


                                       15
<PAGE>   16

all critical materials suppliers by which the Company will implement a
contingency plan that includes alternate sourcing and stockpiling of materials.

Part of the Company's initial assessment phase included a detailed Year 2000
questionnaire which was sent to all critical materials and manufacturing
suppliers. This questionnaire included questions on products, services, internal
operating systems, and the supplier's own supply chain. To date, the Company has
received responses from approximately 95 percent of those questioned. The
Company is following up on the questionnaires, where necessary, with on-site
audits to ensure Year 2000 readiness. The Company has also contacted its major
customers with respect to their Year 2000 readiness efforts and does not believe
that customers will have any Year 2000 readiness problems that would have a
material adverse effect on the Company's business.

In connection with the Company's receipt of transition services pursuant to the
transition agreement with Rockwell, the Company will rely on certain of
Rockwell's computer systems, including its payroll and benefits administration
systems, for a period of up to two years after the Distribution. The Company
believes that the Rockwell systems on which it will rely for transition services
will be Year 2000 ready, such that its reliance thereon will not have a material
adverse effect on the Company's financial position or results of operations.

Conexant, utilizing both internal and external resources to address the Year
2000 issue, expects to be substantially complete with this project by the middle
of calendar year 1999. The current estimate of total project cost is
approximately $6 million, which includes the cost of purchasing certain hardware
and software. Approximately $5 million of this amount is for capital
investments, with the remainder being expenses (primarily salary costs). At
January 1, 1999, approximately $1 million had been spent, with the majority of
the remaining amount to be spent by the end of this year. Conexant continues to
evaluate the estimated costs associated with these efforts based on actual
experience. Management believes, based on available information, that the
Company will be able to remediate Year 2000-related issues in the products,
business systems, and infrastructure areas without any material adverse effect
on its business operations, products, or financial condition. However, the
Company could be adversely impacted by the Year 2000 issues faced by major
suppliers, distributors, customers, vendors, and financial services
organizations with which the Company interacts. Any disruption in the Company's
operations as a result of the failure of any of these third parties to be Year
2000 ready could have a material adverse effect on Conexant's business
operations, products, and financial condition.

CAUTIONARY STATEMENT

This Quarterly Report contains statements relating to future results of the
Company (including certain projections and business trends) that are
"forward-looking statements" as defined in the Private Securities Litigation
Reform Act of 1995. Actual results may differ materially from those projected as
a result of certain risks and uncertainties. These risks and uncertainties
include, but are not limited to: global and market conditions, including, but
not limited to, the cyclical nature of the semiconductor industry and the
markets addressed by the Company's and its customers' products; demand for, and
market acceptance of, new and existing products; successful development of new
products; the timing of new product introductions; the availability and extent
of utilization of manufacturing capacity and raw materials; pricing pressures
and other competitive factors; changes in product mix; fluctuations in
manufacturing yields; product obsolescence; the ability to develop and implement
new technologies and to obtain protection of the related intellectual property;
the successful implementation of the Company's diversification strategy and
restructuring plan; labor relations of the Company, its customers and suppliers;
timely completion of Year 2000 modifications by the Company and its key
suppliers and customers; and the uncertainties of litigation, as well as other
risks and uncertainties, including but not limited to those discussed in the
Company's Registration Statement on Form 10 or detailed from time to time in the
Company's Securities and Exchange Commission filings. Reference is made to the
Risk Factors section on pages 12 to 21 in the Company's Registration Statement
on Form 10, which is incorporated herein by reference. These forward-looking
statements are made only as of the date hereof, and the Company undertakes no
obligation to update or revise the forward-looking statements, whether as a
result of new information, future events or otherwise.


                                       16
<PAGE>   17
ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

Reference is made to the Quantitative and Qualitative Disclosures About Market
Risk section on page 50 in the Company's Registration Statement on Form 10,
which is incorporated herein by reference. The notional amount of all the
Company's outstanding foreign currency forward exchange contracts aggregated
$0.3 million at January 1, 1999, and $17 million at September 30, 1998.

PART II. OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS

On September 27, 1995, Celeritas Technologies, Ltd. filed a suit against
Rockwell in the U.S. District Court for the Central District of California for
patent infringement, misappropriation of trade secrets and breach of contract
relating to cellular telephone data transmission technology utilized in certain
modem products produced by Semiconductor Systems in 1995 and 1996. The court
entered judgment against Rockwell in January 1997 and, in ruling on post-trial
motions in July 1997, entered a revised judgment awarding damages of $57
million, plus interest. On July 20, 1998, the U.S. Court of Appeals for the
Federal Circuit reversed the holding of the trial court based on patent
infringement and found Celeritas' patent invalid but affirmed the trial court
holding based on breach of contract. The Company's petition for a rehearing (and
rehearing en banc) and a motion to certify the contract issue to the California
Supreme Court were denied in September 1998. The Company's petition for
certiorari to the United States Supreme Court filed on November 23, 1998 was
denied in January 1999. At September 30, 1998, $65 million had been accrued for
the ultimate resolution of this matter. Prior to the Distribution, Rockwell paid
into an escrow account $64 million in cash which will be used to satisfy the
Company's obligation with respect to the Celeritas matter.

In connection with the Distribution, the Company assumed responsibility for all
current and future litigation against Rockwell or the Company or their
respective subsidiaries relating to Semiconductor Systems, including those
pertaining to product liability, intellectual property, environmental, safety
and health, and employment matters.

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

Prior to the Distribution, Rockwell, as sole shareholder of the Company and
acting by written consent as permitted by Delaware law, approved the following
matters on the dates indicated: (1) on October 13, 1998, amendment of the
Company's certificate of incorporation to reflect a change in the Company's name
from Rockwell Semiconductor Systems, Inc. to Conexant Systems, Inc.; (2) on
November 4, 1998, adoption by the Company of various benefit plans for the
Company's employees and non-employee directors; (3) on November 17, 1998,
amendment and restatement of the Company's certificate of incorporation; (4) on
November 19, 1998, election of three additional directors and division of the
board of directors into three classes; and (5) on December 2, 1998, adoption by
the Company of an employee stock purchase plan.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

        (a)     Exhibits:

                 3.b    Amended By-Laws of the Company, filed as Exhibit 99.3
                        to the Company's Current Report on Form 8-K dated
                        January 12, 1999, are incorporated herein by reference.

                10.1    Distribution Agreement dated as of December 31, 1998 by
                        and between the Company and Rockwell International
                        Corporation, filed as Exhibit 2.1 to the Company's
                        Current Report on Form 8-K dated January 12, 1999, is
                        incorporated herein by reference.


                                       17
<PAGE>   18

                10.2    Amended and Restated Employee Matters Agreement dated as
                        of December 31, 1998 by and between the Company and
                        Rockwell International Corporation, filed as Exhibit 2.2
                        to the Company's Current Report on Form 8-K dated
                        January 12, 1999, is incorporated herein by reference.

                10.3    Tax Allocation Agreement dated as of December 31, 1998
                        by and between the Company and Rockwell International
                        Corporation, filed as Exhibit 2.3 to the Company's
                        Current Report on Form 8-K dated January 12, 1999, is
                        incorporated herein by reference.

                10.4    Credit Agreement dated as of December 21, 1998 among the
                        Company, the Lenders named therein and Credit Suisse
                        First Boston, as Administrative Agent and Collateral
                        Agent.

                10.5    Employment Agreement dated December 15, 1998 between the
                        Company and B.S. Iyer.*

                10.6    Schedule identifying agreements substantially identical
                        to the Employment Agreement constituting Exhibit 10.5
                        hereto entered into by the Company with M.M. Beguwala, 
                        L.C. Brewster, A.C. D'Augustine, T.L. Ellis, R.Y. Halim,
                        D.E. O'Reilly, A. Rangan, F.M. Rhodes, J.P. Spoto, T.A.
                        Stites, K.V. Strong and W.C. Tipton.*

                10.7    Employment Agreement dated December 15, 1998 between the
                        Company and D.W. Decker.*

                27      Financial Data Schedule.

        (b)     Reports on Form 8-K:

                        The Company filed a current report on Form 8-K dated
                January 12, 1999, in respect of the completion on December 31,
                1998, of the spin-off of Rockwell's Semiconductor Systems
                business to holders of shares of Common Stock, par value $1 per
                share, of Rockwell by means of the distribution to such holders
                of all outstanding shares of Common Stock, par value $1 per
                share (including the preferred share purchase rights associated
                with such Common Stock), of the Company (Items 5 and 7(c)).

                The Company filed a current report on Form 8-K dated January 20,
                1999, in respect of the Company's press release reporting
                earnings for the three-months ended January 1, 1999 (Items 5
                and 7(c)).


--------
* Indicates that the exhibit is a management contract or compensatory plan or
  arrangement.


                                       18
<PAGE>   19

                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                                              CONEXANT SYSTEMS, INC.
                                              (Registrant)




Date     February 10, 1999                    By /s/ STEVEN M. THOMSON
                                                 -------------------------------
                                                 Steven M. Thomson
                                                 Vice President and Controller
                                                 (Principal Accounting Officer)




Date     February 10, 1999                    By /s/ DENNIS E. O'REILLY
                                                 -------------------------------
                                                 Dennis E. O'Reilly
                                                 Senior Vice President,
                                                 General Counsel and Secretary


                                       19
<PAGE>   20

                                  EXHIBIT INDEX

<TABLE>
<CAPTION>
                                                                                        Sequentially
Exhibit                                                                                 Numbered Page
-------                                                                                 -------------
<C>               <S>
 3.b              Amended By-Laws of the Company, filed as Exhibit 99.3 to the
                  Company's Current Report on Form 8-K dated January 12, 1999,
                  are incorporated herein by reference.

10.1              Distribution Agreement dated as of December 31, 1998 by and
                  between the Company and Rockwell International Corporation,
                  filed as Exhibit 2.1 to the Company's Current Report on Form
                  8-K dated January 12, 1999, is incorporated herein by
                  reference.

10.2              Amended and Restated Employee Matters Agreement dated as of
                  December 31, 1998 by and between the Company and Rockwell
                  International Corporation, filed as Exhibit 2.2 to the
                  Company's Current Report on Form 8-K dated January 12, 1999,
                  is incorporated herein by reference.

10.3              Tax Allocation Agreement dated as of December 31, 1998 by and
                  between the Company and Rockwell International Corporation,
                  filed as Exhibit 2.3 to the Company's Current Report on Form
                  8-K dated January 12, 1999, is hereby incorporated herein by
                  reference.

10.4              Credit Agreement dated as of December 21, 1998 among the
                  Company, the Lenders named therein and Credit Suisse First
                  Boston, as Administrative Agent and Collateral Agent.

10.5              Employment Agreement dated December 15, 1998 between the 
                  Company and B.S. Iyer.*

10.6              Schedule identifying agreements substantially identical to the
                  Employment Agreement constituting Exhibit 10.5 hereto entered
                  into by the Company with M.M. Beguwala, L.C. Brewster, A.C. 
                  D'Augustine, T.L. Ellis, R.Y. Halim, D.E. O'Reilly, A. Rangan,
                  F.M. Rhodes, J.P. Spoto, T.A. Stites, K.V. Strong and W.C. 
                  Tipton.*

10.7              Employment Agreement dated December 15, 1998 between the 
                  Company and D.W. Decker.*

27                Financial Data Schedule.
</TABLE>


--------
* Indicates that the exhibit is a management contract or compensatory plan or
  arrangement.