<PAGE>   1

                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 10-Q

 (Mark One)

 __X__   Quarterly report pursuant to Section 13 or 15(d) of the Securities
         Exchange Act of 1934.  For the quarterly period ended March 30,
         1997.

______   Transition report pursuant to Section 13 or 15(d) of the Securities
         Exchange Act of 1934.  For the transition period from _____________
         to ____________.

                        Commission File Number:  0-18738
                                                 -------

                                  ZILOG, INC.
                                  (Registrant)

               California                                13-3092996
     -------------------------------         -----------------------------------
     (State or other jurisdiction of         (I.R.S Employer Identification No.)
     incorporation or organization)

          210 East Hacienda Avenue, Campbell, California, 95008-6600  
          ----------------------------------------------------------
                    (Address of principal executive offices)

      Registrant's telephone number, including area code:  (408) 370-8000


         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   X      No
                                -----       -----



 20,216,136 shares of Common Stock Issued and Outstanding as of April 27, 1997.
<PAGE>   2
Part I.  FINANCIAL INFORMATION
Item 1.  Financial Statements



                                  ZILOG, INC.
            CONDENSED CONSOLIDATED STATEMENTS OF INCOME (Unaudited)
                    (in thousands, except per share amounts)


<TABLE>
<CAPTION>
                                                             Three Months Ended
                                                          ------------------------
                                                          March 30,      March 31,
                                                            1997           1996 
                                                            ----           -----
<S>                                                       <C>             <C>
Sales                                                     $ 70,136        $ 80,999

Costs and expenses:
  Cost of sales                                             44,028          42,941
  Research and development                                   6,632           7,587
  Selling, general and administrative                       12,052          12,037
                                                          --------        --------
                                                            62,712          62,565
                                                          --------        --------

Operating income                                             7,424          18,434

Other income (expense):
  Interest income                                              664             733
  Interest expense                                             (69)           (811)
  Other, net                                                  (880)           (368)
                                                          --------        -------- 

Income before income taxes                                   7,139          18,718

Provision for income taxes                                   2,356           6,645
                                                          --------        --------

Net income                                                $  4,783        $ 12,073
                                                          ========        --------

Net income per share                                         $0.23           $0.59
                                                             =====           =====

Number of shares used in computing per
share amounts                                               20,901          20,424
                                                           =======         =======
</TABLE>


                            See accompanying notes.





                                       2
<PAGE>   3
                                  ZILOG, INC.
                     CONDENSED CONSOLIDATED BALANCE SHEETS
                             (dollars in thousands)
<TABLE>
<CAPTION>
                                                                             March 30,         December 31,
                                                                               1997                1996
                                                                               ----                ----
                                                                            (Unaudited)
<S>                                                                          <C>                  <C>
                                              ASSETS
Current assets:
  Cash and cash equivalents                                                  $ 11,596             $ 15,511
  Short-term investments                                                       56,937               53,412
  Accounts receivable, less allowance for doubtful
     accounts of $250 in 1997 and 1996                                         32,776               29,395
  Inventories                                                                  32,013               34,469
  Prepaid expenses, deferred income taxes and
     other current assets                                                      16.018               15,516
                                                                             --------             --------
          Total current assets                                                149,340              148,303

Property, plant and equipment, at cost                                        391,759              379,928
Less: accumulated depreciation and amortization                              (146,043)            (131,217)
                                                                             --------             ---------
   Net property, plant and equipment                                          245,716              248,711
Other assets                                                                    3,489                4,052
                                                                             --------             --------
                                                                             $398,545             $401,066
                                                                             ========             -=======

                                LIABILITIES AND SHAREHOLDERS' EQUITY
Current liabilities:
  Accounts payable                                                           $ 21,795             $ 28,786
  Accrued compensation and employee benefits                                   15,182               17,545
  Other accrued liabilities                                                     4,690                5,116
  Income taxes payable                                                         10,265                8,289
                                                                             --------             --------
          Total current liabilities                                            51,932               59,736

Deferred income taxes                                                          16,050               16,050

Shareholders' equity:
  Common Stock, no par value; 75,000,000 shares
    authorized; 20,159,646 shares issued and
    outstanding at March 30, 1997 (20,127,976 shares
    at December 31, 1996)                                                     162,242              161,800
 Retained earning                                                             168,158              163,375
 Net unrealized gain on securities                                                163                  105
                                                                             --------             --------
          Total shareholders' equity                                          330,563              325,280
                                                                             --------             --------
                                                                             $398,545             $401,066
                                                                             ========             ========
</TABLE>

                            See accompanying notes.





                                       3
<PAGE>   4
                                  ZILOG, INC.
          CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited)
                Increase (decrease) in cash and cash equivalents
                             (dollars in thousands)
<TABLE>
<CAPTION>
                                                                                 Three  months ended
                                                                            -----------------------------
                                                                            March 30,           March 31,
                                                                               1997                1996
                                                                               ----                ----
<S>                                                                          <C>                 <C>
Cash flows from operating activities:
 Net income                                                                  $  4,783            $ 12,073
  Adjustments to reconcile net income to cash
  provided by operating activities:
     Depreciation and amortization                                             15,150               9,990
     Loss from disposition of equipment                                             3                  95
  Changes in assets and liabilities:
     Accounts receivable                                                       (3,381)                614
     Inventories                                                                2,456              (5,106)
     Prepaid expenses, deferred income taxes and
       other assets                                                                26              (2,148)
     Accounts payable                                                          (6,991)                525
     Accrued compensation and employee benefits                                (2,363)             (2,674)
     Other accrued liabilities and income taxes payable                         1,550               5,585
                                                                             --------            --------
     Cash provided by operating activities                                     11,233              18,954

Cash flows from investing activities:
   Capital expenditures                                                       (11,991)            (38,535)
   Short-term investments:
     Purchases                                                                (10,755)             (5,964)
     Proceeds from sales                                                        7,156              17,958
     Proceeds from maturities                                                       -               3,523
                                                                             --------            --------
          Cash used for investing activities                                  (15,590)            (23,018)
                                                                             --------            -------- 
Cash flows from financing activities:
  Proceeds from issuance of stock                                                 442               3,386 
                                                                             --------            --------

Decrease in cash and cash equivalents                                          (3,915)               (678)
Cash and cash equivalents at beginning of period                               15,511               7,784
                                                                             --------            --------

Cash and cash equivalents at end of period                                   $ 11,596            $  7,106
                                                                             ========            ========
</TABLE>


                            See accompanying notes.





                                       4
<PAGE>   5
                                  ZILOG,  INC.

Notes To Consolidated Financial Statements (Unaudited)

1)  Interim information is unaudited; however, in the opinion of the Company's
    management, all adjustments (consisting only of normal recurring
    adjustments), necessary for a fair statement of interim results have been
    included.  The results for interim periods are not necessarily indicative
    of results to be expected for the entire year.  These financial statements
    and notes should be read in conjunction with the Company's annual
    consolidated financial statements and notes thereto contained in the
    Company's Annual Report to Shareholders and the Company's Annual Report on
    Form 10-K for the year ended December 31, 1996.  The Consolidated Balance
    Sheet at December 31, 1996 has been derived from audited financial
    statements at that date.

2)  The following is a summary of total securities, which are all held as
    available-for-sale (in thousands):

<TABLE>
<CAPTION>
                                                       March 30, 1997
                                   ------------------------------------------------------
                                                   Gross          Gross         Estimated
                                    Cost        Unrealized      Unrealized        Fair
                                                   Gains          Losses          Value
                                   ------------------------------------------------------
    <S>                            <C>             <C>             <C>           <C>
    Municipal Bonds                $54,695         $252            $  -          $54,947
    U.S. government  and
          agency securities          1,991            -              (1)           1,990
                                   ------------------------------------------------------
                                   $56,686         $252            $ (1)         $56,937
                                   ======================================================
</TABLE>


    The gross realized gains and losses on sales have not been material for
    the quarters ended March 30, 1997 and March 31, 1996.

    The amortized cost and estimated fair value of marketable debt securities
    are shown below (in thousands):

<TABLE>
<CAPTION>
                                                      March 30, 1997
                                                  ----------------------
                                                                Estimated
                                                   Cost           Fair
                                                                  Value
                                                  -------        -------
    <S>                                           <C>            <C>
    Due in 1 year or less                         $33,227        $33,320
    Due after 1 year through 3 years               20,344         20,494
    Due after 3 years                               3,115          3,123
                                                  -------        -------
    Total debt securities                         $56,686        $56,937
                                                  =======        =======
</TABLE>





                                       5
<PAGE>   6
3)  The components of inventories are as follows (in thousands):

<TABLE>
<CAPTION>
                                         Mar. 30,       Dec. 31,
                                           1997           1996
                                           ----           ----
           <S>                            <C>            <C>
           Raw Materials                  $ 5,237        $ 5,385
           Work-in-process                 22,169         23,412
           Finished goods                   4,607          5,672
                                          -------        -------
                                          $32,013        $34,469
                                          =======        =======
</TABLE>

4)  In February 1997, the Financial Accounting Standards Board issued Statement
    No. 128, Earnings per Share, which is required to be adopted on December
    31, 1997.  At that time, the Company will be required to change the method
    currently used to compute earnings per share and to restate all prior
    periods.  Under the new requirements for calculating primary earnings per
    share, the dilutive effect of stock options will be excluded.  Basic EPS
    calculated in accordance with Statement No. 128 would be greater than net
    income per share for the first quarter ended March 30, 1997 and March 31,
    1996 by $.01 and $.03 per share, respectively.  Diluted earnings per share
    for these quarters is expected to approximate net income per share as
    reported.








Private Securities Litigation Reform Act Safe Harbor Statement:

         When used in this Report, the words "estimate," "project,"
"intend," and "expect" and similar expressions are intended to identify
forward-looking statements.  Such statements are subject to risks and
uncertainties that could cause actual results to differ materially.  For a
discussion of certain of such risks, see "Factors That May Affect Future
Results."  Readers are cautioned not to place undue reliance on these
forward-looking statements, which speak only as of the date hereof.  The
Company undertakes no obligation to publicly release updates or revisions to
these statements.





                                       6
<PAGE>   7
Part I.  FINANCIAL INFORMATION

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



The following table presents unaudited results.  The Company believes that all
necessary adjustments, consisting only of normal recurring adjustments, have
been included in the amounts shown below to state fairly the selected quarterly
information when read in conjunction with the Consolidated Financial Statements
included elsewhere herein.  Interim results are based on fiscal quarters of
thirteen weeks in duration ending on the last Sunday of each quarter.  The
operating results for any quarter are not necessarily indicative of results for
any subsequent quarter or the full fiscal year.  All tabular information is
provided in thousands, except per share amounts and percentages.


Results of Operations

<TABLE>
<CAPTION>
                                     First         First
                                    Quarter       Quarter       Change
                                     1997          1996
                                    -------       -------       -------
<S>                                 <C>           <C>           <C>
Sales                               $70,136       $80,999       (13.4%)
Operating Income                    $ 7,424       $18,434       (59.7%)
Net Income                          $ 4,783       $12,073       (60.4%)
Net Income Per Share                $  0.23       $  0.59       (61.0%)
</TABLE>

Sales

         The Company's quarterly operating results have and will vary because
of a number of factors, including the timing and success of new product
introductions, changes in product mix, volume, timing and shipment of orders
and fluctuations in manufacturing productivity.  Quarter-to-quarter sales
comparisons are also subject to customer order patterns and seasonality.
Because the Company's products are available from both the Company and
distributors, the customer's decision to buy from a distributor or directly
from the Company can affect Zilog's quarterly sales and profitability.  See
"Factors That May Affect Future Results" for a discussion of additional
considerations which may affect the Company's future operating results.





                                       7
<PAGE>   8
         Sales decreased 13.4% for the first quarter of 1997 from the
comparable quarter of 1996, primarily because of lower modem sales in the
datacommunications market and declines in printer sales in the computer
peripherals market.  Revenue in the consumer market increased during the first
quarter as a result of higher television and infrared (IR) remote sales.

         Overall unit volumes increased for the first quarter of 1997 compared
to the same period of 1996.  Volume growth, however, was offset by lower
average selling prices resulting from a shift in the Company's product mix.
During the first quarter of 1997, over-capacity in the industry led to price
pressure and declines in the Company's average selling prices.  The Company is
uncertain for how long this trend may continue.  Domestic sales accounted for
38.0% of revenues in 1997, representing a decrease of 32.3% in the first
quarter compared to the same period of 1996.  International sales were 62.0% of
revenues in the first quarter of 1997, representing an increase of 4.5% from
the comparable quarter of 1996.  The fastest growing international areas are
Hong Kong and Singapore.


<TABLE>
<CAPTION>
                                     First         First
                                    Quarter       Quarter        Change
                                     1997          1996
                                    -------       -------        ------
<S>                                 <C>           <C>             <C>
Cost of Sales                       $44,028       $42,941         2.5%
Percentage of Sales                   62.8%         53.0%
</TABLE>


         The Company's cost of sales represents the cost of its wafer
fabrication, assembly and test operations.  Cost of sales fluctuates, depending
on manufacturing productivity, product mix, equipment utilization and
depreciation.  Cost of sales increased in the first quarter of 1997 as a
percentage of sales to 62.8% from 53.0%.  The increase in the percentage of
cost of sales to sales in the first quarter of 1997 compared to the first
quarter of 1996 was primarily attributable to a decrease in revenue, lower
equipment utilization of the fabrication facility and added depreciation.  The
increase in the percentage of cost of sales was partially offset by lower
foundry costs.  Depreciation arising from the Company's fabrication facility
are expected to increase through the first half of 1997.  The financial impact
of the additional depreciation will be, in part, determined by the volume of
products produced and the overall efficiency of the fabrication facilities.


<TABLE>
<CAPTION>
                                    First          First
                                   Quarter        Quarter         Change
                                     1997          1996
                                   -------        -------        --------
<S>                                 <C>           <C>            <C>
Research and Development            $6,632        $7,587         (12.6%)
Percentage of  Sales                  9.5%          9.4%
</TABLE>





                                       8
<PAGE>   9
         Research and development expenditures decreased during the first
quarter of 1997 in absolute dollars but increased as a percentage of sales when
compared to the same period of 1996.  The decrease in research and development
dollars for the first quarter of 1997 resulted from the Company's exercising
tight expense controls over outside consulting services and process
engineering costs in the start up of its new fabrication facility.

         The Company introduced 12 new products during the quarter.  Of these,
10 products were for the consumer market, one for the computer peripherals
market and one for the datacommunications market.

         The Company plans to invest a major portion of its estimated $50
million capital expenditures budget for 1997 in a new research facility with
the capability of designing to a .35 micron feature size in mixed signal
processes.  The Company believes that achieving commercial production of this
process will be important to continued introduction of new products in its
chosen markets.  The Company remains committed to new product development and
manufacturing process technology.


<TABLE>
<CAPTION>
                                             First         First
                                            Quarter       Quarter       Change
                                             1997          1996
                                            -------       -------       ------
<S>                                         <C>           <C>            <C>
Selling, General & Administrative           $12,052       $12,037        0.1%
Percentage of Sales                          17.2%         14.9%
</TABLE>



         Selling, general and administrative expenses remained essentially the
same in absolute terms but increased as a percentage of  sales.  The increase
in selling, general and administrative expenses as a percentage of sales in the
first quarter of 1997, as compared to the same period in 1996, is attributable
to lower sales in 1997.  Selling, general and administrative costs should
increase in absolute terms but decrease as a percentage of sales during 1997 if
sales grow as expected.


<TABLE>
<CAPTION>
                                             First         First
                                            Quarter       Quarter       Change
                                              1997         1996
                                            -------       -------       --------
<S>                                          <C>           <C>          <C>
Other Income (Expense), net                  $(285)        $284         (200.4)%
Percentage of Sales                          (0.4)%        0.4%
</TABLE>





                                       9
<PAGE>   10
         Other income (expense), net declined to $285,000 in expenses in the
first quarter of 1997 from $284,000 of income for the same period in 1996.  The
primary reason for the decline was that the Company received lower royalty
income during the first quarter of 1997 because a licensee withheld royalty
payments while renegotiating an extension of its license agreement.  The
license agreement is currently being renegotiated and the Company expects that
the royalty income will be paid for all royalties now owed during the second
quarter of 1997.  Royalty income is dependent on end user volume and can vary
significantly from quarter to quarter.


Taxes

         The provision for income taxes was 33.0% for the first quarter of 1997
compared to 35.5% for the same period of 1996.  The lower tax provision for
1997 is primarily attributable to a larger impact of tax exempt revenue and
foreign income taxed at a lower than U.S. rate.


Factors That May Affect Future Results

         A number of uncertainties exist that may affect the Company's future
operating results, including uncertain political and general economic
conditions, market acceptance of the Company's new products, the Company's
ability to introduce new products and technologies on a timely basis, changes
in product mix or fluctuations in manufacturing yield that affect the
Company's gross margins, and numerous competitive factors.

         The present increased activity in mergers and acquisitions in the
electronics marketplace involves Zilog's customers.  When such mergers and
acquisitions occur, there may be some interruption in customer ordering
patterns as inventories are rebalanced, or the historic Zilog revenue stream
with the customer may change significantly as new ownership redirects marketing
priorities.

         During 1996, Zilog introduced a total of 48 new products for its
datacommunications, intelligent peripheral controller and consumer product
lines.  The success of these new products is dependent on a number of factors,
including the Company's ability to continue to achieve design wins for these
products and the Company's ability to manufacture the products in sufficient
quantities to meet anticipated demand.  New products may exhibit technological
defects which may impede market acceptance if defects are not resolved
promptly.  The Company believes that a significant portion of its future
revenues will come from these new products.  Gross margins for new products are
generally higher and are expected to somewhat offset price reductions in older
products.

         The Company's operating results will depend, to a significant extent,
on its ability to continue to introduce new products.  The success of new
product introductions is dependent on several factors, including proper new
product selection, timely completion and introduction of new product designs,
development of support tools and collateral literature that make complex new
products easy for engineers to understand as well as use, and market acceptance
of customers' end products.





                                       10
<PAGE>   11
         During the first quarter of 1997, Zilog introduced 12 new products.
There can be no assurance that any new products will receive or maintain
substantial market acceptance, nor can there be assurance that the Company will
continue to introduce new products at a similar pace to that established over
the past year.

         Operating results could be adversely affected if the Company is unable
to develop and implement new design and process technologies.  Design and
process technology advances are extremely complex areas subject to rapid
technological change and significant risk.  New product designs must be
completed in time to meet market requirements, and volume production of new
products at acceptable yields must be achieved for business plan operating
results to be realized.  New products anticipated from and introduced by Zilog
could create uncertainty in the marketplace and cause customers to defer or
alter design wins or purchasing decisions.  Additionally, new products or
product enhancements from competitors of the Company, or significant pricing
pressures, could have an adverse impact on the Company's operating results.

         As is typical in the semiconductor industry, the Company has from time
to time experienced lower than anticipated production yields.  Operating
results could be adversely affected if any problems occur that make it
difficult to produce the quantities of commercial product that the Company
anticipates producing in its Mod III facility and its new research and
development fabrication line expected to begin operations in 1997.  Such
difficulties include but are not limited to: equipment being delivered later
than or not performing as expected; process technology changes not operating as
expected; engineers not operating equipment as expected; and other possible
problems.  The Company cannot at this time foresee with certainty any such
problems, but such problems have occurred in the past in the start-up and ramp
of production in new facilities.  The Company is also experiencing certain
inflationary pressures in labor and materials.  Operating results could be
affected if the Company is unable to pass these cost increases in labor, raw
materials and capital equipment through to the Company's customers.

         The Company has used outside wafer foundries and assemblers to supply
a portion of its manufacturing needs, and the Company expects to continue to
rely on one or more wafer foundries and assemblers for a portion of its
manufacturing needs.  No assurance can be given that these foundries will not
raise prices or meet expected delivery quantities.  In addition, no assurance
can be given that the Company or its outside wafer foundries or assemblers will
not experience production yield problems in the future which could result in an
adverse effect on the Company's results of operations.  The prolonged failure
of the Company to increase production capacity, obtain wafers or assembly
services from outside suppliers as needed could adversely affect the Company's
operating results.

         Certain of the Company's products are incorporated into disk drives,
printers, keyboards and modems.  As a result, a slowdown in the demand for
personal computers and related peripherals could adversely affect the
Company's operating results.  A significant portion of the Company's sales are
to the consumer electronics markets for use in products such as television
sets, infrared remote controls and telephone answering machines.  The consumer
electronics markets are subject to volatile and rapid changes in customer
preferences for electronics products that could adversely impact the Company's
results.





                                       11
<PAGE>   12
         Because of the foregoing, as well as other factors affecting the
Company's operating results, past financial performance should not be
considered to be a reliable indicator of future performance, and investors
should not use historical trends to anticipate results or trends in future
periods.  In addition, the Company participates in a highly dynamic industry
that may result in significant volatility of Zilog's common stock price.

Liquidity and Capital Resources

<TABLE>
<CAPTION>
                                                     First         First
                                                    Quarter       Quarter
                                                     1997          1996
                                                    -------       -------
<S>                                                 <C>           <C>
Cash, Cash Equivalents and
   Short-Term Investments                           $68,533       $65,059
Working Capital                                     $97,408       $89,177
Cash Provided By Operating Activities               $11,233       $18,954
Cash Used In Investing Activities                  ($15,590)     ($23,018)
Cash Provided By Financing Activities               $   442       $ 3,386
</TABLE>

         Cash and Short-Term Investments increased to $68.5 million for the
first quarter of 1997 from $65.1 million in the same period of 1996.  Accounts
receivables increased slightly to $32.8 million in the first quarter of 1997
from $29.4 million in the same quarter of 1996.  Inventory levels decreased
slightly to $32.0 million due to the Company carrying less raw materials, 
work-in-process and finished goods.

         The Company expects to make total capital additions of approximately
$50 million in 1997.  These expenditures will primarily be used for the design,
construction and equipping of the Company's new wafer fabrication and research
facility in Nampa, Idaho and other engineering capital expenditures.  The
expansion will provide increased production capacity and research facilities.

         The Company believes its current cash, cash equivalents and short-term
investment balances, together with funds expected to be generated from
operations, will provide adequate cash to fund the Company's anticipated
liquidity needs for at least the next twelve months.  The Company may also use
bank borrowings and capital leases, depending on the terms available.  The
Company's cash requirements in the future may also be financed by a
combination of additional equity or debt financing.





                                       12
<PAGE>   13
Part II.  Other Information

Item 6.  Exhibits and Reports on Form 8-K

a)  The following exhibit is filed herewith:
         Exhibit 27 Financial Data Schedule

b)   Reports on Form 8-K:
         None





                                       13
<PAGE>   14
                                  ZILOG, INC.

                                   SIGNATURES

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




Date:  May 12, 1997                                 ZILOG, INC.


                                              /s/  Robert E. Collins            
                                        ----------------------------------
                                                   Robert E. Collins
                                                  Vice President and
                                                Chief Financial Officer





                                       14
<PAGE>   15
                                 EXHIBIT INDEX


<TABLE>
<CAPTION>
EXHIBIT  
  NO.          DESCRIPTION
-------        -----------
 <S>           <C>
 27            Financial Data Schedule
</TABLE>