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Maybe... probably not. IBM was looking for a small company they could control. They can and did pretty much write DOS on their own. IBM funded around 99% of the effort. Microsoft was just the contractor IBM used to circumvent being split up like Ma-Bell.
Digital Research was only 6 guys. They had the CP/M OS from the Zilog Z80 which was selling well, which is why IBM turned to them. BUT they had to upscale it to a 16 bit OS.
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But there are many somewhat conflicting stories about what happened when IBM went to meet with Digital Research. Gates is quoted in
Fire in the Valley as saying "Gary was out flying" that day, but Kildall always denied the implication, telling the authors of
Hard Drive that he had flown on a business trip to the Bay Area.
IBM and its lawyers met with Kildall's wife, Dorothy McEwen, and presented Digital Research with a one-sided non-disclosure agreement, which the company refused to sign. Later, Sams would tell the authors of
Hard Drive that IBM just couldn't get Kildall to agree to spend the money to develop a 16-bit version of CP/M in the tight schedule IBM required. But whatever the reason, it's clear that IBM left Digital Research without an agreement on an operating system.
IBM communicated its problem to Microsoft later that month, and Microsoft's Gates, Paul Allen, and Kay Nishi apparently debated what to do about the program. Allen knew of an alternative: Tim Paterson of Seattle Computer Products (SCP) had earlier built an 8086-based prototype computer and while he was waiting for CP/M to be ported to the 8086, he created a rough 16-bit operating system for it. Paterson called it QDOS for Quick and Dirty Operating System, and according to Allen, it all fit within 6K. (It would later be renamed 86-DOS, and sometimes referred to as SCP-DOS.)}
The Rise of DOS How Microsoft Got the IBM PC OS Contract