There's a sort of urban legend among people I've spoken to about Sinclair that the Executive calculator can't divide by 0. Specifically, if you do this then it goes into a busy loop, cannot be used, and drains/overheats the batteries until they run out or explode. There is an attested story of the cells overheating due to the calculator being left on, but I can't find any evidence that it would become unusable as a result of dividing by zero.
What I can find is that the manual for mine, which is the earlier model with the K switch (serial 19216), describes various overflow conditions and that when they occur, you clear the calculator and start again. I can't test this as I don't have the correct cells to use it.
Also this description of the TMS1802 says that pin 13/D11 is used for overflow and error signalling, which implies that overflow detection is part of the chip. So even if it didn't have /0 protection, it would be able to signal the error and let the user clear/restart.
So is there any truth to the rumour that you could render a Sinclair Executive unusable by dividing by zero? Was there a different electronic calculator that did exhibit that sort of behaviour? I know that mechanical calculators can get into infinite loops when trying that.