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Reeling from troubles with numbers, executives at Intel Corp., maker of the notoriously flawed Pentium computer chip, said Tuesday that they hope this toll-free phone number will save the company from one of the decade’s worst public relations gaffes.

Effective at the start of business Wednesday, any Pentium owner upset that the superchip fails to give correct answers when dividing certain large numbers will get a corrected chip free of charge, company officials said.

And there will be no questions asked, promised Andrew Grove, chief executive of the Santa Clara, Calif.-based company, in a conference call with reporters and stock analysts Tuesday.

It was, noted leading computer industry analysts, such as David Wu of S.G. Warburg Inc., a complete reversal from the company’s widely condemned prior policy.

Heretofore, Pentium owners had to prove their machines were used for extremely complex scientific or financial computations before getting a replacement chip.

Tuesday’s “no-questions-asked” capitulation by Intel was the latest development in a flap that has raged for a month.

It spread from the rarefied laboratories of university mathematicians to the living and recreation rooms of families playing with a new generation of Pentium-based multimedia home computers.

Just before Thanksgiving, the general public learned that the superchip by Intel, which is replacing the 486 line of chips for IBM-compatible personal computers on 50 million desktops worldwide, makes errors dividing certain large numbers.

For example, when a Pentium divides 5,505,001 by 294,911, it gets the answer 18.66600; the real answer is 18.66665.

Intel downplayed the significance of such errors.

The company’s scientists pointed out that the chances a given computer owner might come up with a situation where 5,505,001 was divided by 294,911 were extremely remote.

And even then, said the company, the error, which didn’t appear until the fourth decimal place, was unimportant to the vast majority of computer users. There was, said Intel, only 1 chance in 9 billion that any computer owner would encounter a problem with the flaw.

For that reason, Intel insisted it would only replace chips for heavy-duty computer users such as NASA space-flight planners and theoretical mathematicians with extraordinary needs for precision.

The company rejected repeated objections from computer experts who argued that many calculations take the fourth decimal place into consideration. For example, some companies compute employee raises down to the fourth decimal.

Intel countered that the vast majority of calculations that go to the fourth decimal would be unaffected, that only a few specific large numbers cause the error and that the chance of ever needing to use them was highly remote.

The hard-nosed stance created a firestorm of complaints from owners of computers based on the new chip and kept the Pentium issue on the front burner for weeks.

Computer scientists pelted Intel with charges that the company was being arrogant and evasive. Home computer buyers expressed dismay that their costly new machines might have been terrible investments.

The chip story became a mother lode of jokes for stand-up comics: “How can you tell your computer is dangerous? By the `Intel Inside’ warning on the box.”

Alluding to the anger and the ridicule, Grove told Tuesday’s session with representatives of the world’s leading brokerage houses, “The past few weeks have been deeply troubling. What we continue to view as an extremely minor technical problem has taken on a life of its own.”

He added, “We were motivated by a belief that replacement is simply unnecessary for most people. We still feel that way, but we are changing our policy because we want there to be no doubt that we stand behind this product.”

Grove told the analysts the offer could be enormously expensive if large numbers of Pentium owners take him up on it.

As a result, he said, Intel will take an as-yet-unspecified charge against fourth-quarter earnings to cover the costs. The current consensus among analysts polled by Zack’s Investment Research in Chicago is that Intel will earn $1.56 a share this quarter. Analysts speculate that the recall will cost the company 15 to 20 cents a share. Intel would say only that the cost would likely be more than 5 cents a share.

Intel has made nearly 6 million of the flawed chips. Company sources estimate that 2 million of those have been sold in this holiday season.

Flanked by the company’s top executives, Grove outlined a bizarre situation in which Intel over the next two months will continue to produce flawed Pentium chips on some assembly lines while turning out good chips on other assembly lines at its complex of factories in California, New Mexico and Texas.

Even as the bad chips come off the assembly lines and go into newly built computers, the company will take phone requests from owners of flawed Pentiums to replace them with corrected chips, called “clean” ones in the industry.

Grove said that by the start of the first quarter of 1995, 50 percent of the chips being produced will be clean, and that by the end of the quarter all the Pentiums being produced will be clean.

Thus, he said, the public’s response to the replacement offer could have a massive impact or a minor one on Intel’s revenues.

He said that based on past experience, Intel expects that only a small fraction of Pentium owners will actually go through the process and acquire a replacement chip.

The process starts with calling the 800 number and discussing replacement plans with a technician. Callers will be given the option of getting a new chip and written instructions for replacing the old one, or they can disconnect their computer from the printer, modem and monitor and take it to a service center to have an expert install a new chip.

Callers also will be required to give a credit card number for a deposit of $495 to $995 to ensure that they return the flawed chip once the new one is in place.

Although Grove declined to discuss specific numbers, company officials informally confirmed that the cost of an individual Pentium chip to the end user is $400 to $600. Each chip costs Intel $50 to $150 to make, not including development costs.

With Intel making and selling Pentiums at full throttle, every chip replaced will be a Pentium it could otherwise sell to a new user. That means the potential lost revenue would be around $300 million if just 10 percent of the owners of the 6 million flawed Pentiums demand a refund. If all eligible owners take the company up on its offer, the lost revenue could hover around $3 billion.

For all of last year, Intel earned $2.3 billion on sales of $8.78 billion.

Wu, the Intel analyst at S.G. Warburg, issued a report in the wake of the Intel policy reversal predicting that the company will have a “soft” first quarter in 1995 because of the Pentium problem, but concluding that the company will continue to flourish.

“Our current checks with a number of PC companies and resellers confirms no slowdown in the retail channel, which is currently extremely strong,” the report said. It concluded, “BUY-1995 is still the year of the Pentium, but. . .”