An important customer had been sold a networking processor deal which would need custom software modifications to handle the number of terminals they required.
The project manager asked me to look at the proposal - at which point it was obvious that there was a problem. Due to a quirk of the cpu instruction set - the code would not be able to handle the size of the data structures.
Most instruction modes simply addressed 0-64k - but one mode allowed an offset of -32k to +32k in calculating a final address. If the offset went above +32k there was an exception interrupt. This mode was unfortunately the one used to address the terminal data structures in this system - and there was no way anyone was going to redesign the system software.
I told the hardware design engineers that if they inhibited the exception interrupt then the existing software would still work - and the size of the terminal data structure could be increased. The only possible penalty was a missed exception - but on inspection no one had used the negative offset capability in the system software
It then came as a surprise to me that the hardware design engineer didn't recognise that binary negative numbers are also positive numbers. So I set up a little demonstration to show the basic principles of twos complement arithmetic. That convinced him. In those days many hardware engineers regarded cpu design as a specialised field - most of them just did logic.
It was still a relief to me several months later when the modified software worked perfectly ahead of the customer's "must do" schedule. It had a cpu board which contained the mod of a switch to disable that exception interrupt.
The project was make or break for retaining that important mainframe customer - who was then a very happy bunny. The company suggestion scheme gave me £50 for "a good idea of limited use".